Differentiation : Tangents and Normals : ExamSolutions

Tutorial on differentiation to find tangents and normals to a function.
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[@HenriBorov]

I understand this after you teaching for 8min better than I did after and hour lesson with my teacher. thank you so much

[@shreythedriver]

9th grader here... Same with me

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Shreyansh Chakranarayan weird flex but ok

[@snhtsljedc9803]

I comment regularly on your videos and I can’t thank you enough for everything you have helped me with like honestly, you have taught me the whole of differentiation in less than an hour

[@ExamSolutions_Maths]

Thank you too for continuing to show your support and appreciation. Best wishes.

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[@cypher4528]

My math exam was tomorrow, I couldn't even understand the base of this 'Tangents and Normals' because I didn't go to school, but your 8 mind of teaching helped me understand basics very easily

[@ExamSolutions_Maths]

I wish you every success.

[@TheGreatBrendon]

thank you for taking the time to make this video. really great work

[@MrEric-rs2wg]

Easiest way of Teaching Tangents & Normals in terms of Differentiation.. Good job

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[@ExamSolutions_Maths]

No probs. Pleased to hear it helped.

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[@mostafakamaly]

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[@leeleelaka]

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[@starshain]

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[@ExamSolutions_Maths]

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[@chisommefor686]

I love you so much. Thank you.

[@ExamSolutions_Maths]

@adirajuadithya Tangents don't necessarily have lengths. It is just a line drawn to the edge of a curve.

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[@samgirl964]

Thankyou!

[@sheramann1881]

Hi. if you had the curve to include another x, say for example: x^3 + x + 1, would the gradient be 3X + 1? Or would you have to differentiate further such that the gradient is 6x?

[@frdashhriani]

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[@ExamSolutions_Maths]

@mostafakamaly Yes - Just go on my website and look under the main index of tutorials

[@limweewen2803]

Thank you this is very easy to understand and very useful

[@ExamSolutions_Maths]

Thanks for watching - pleased it helped.

[@muzshar123]

Thankssss :)

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[@catalinavazquez2530]

thank you so much for the explanation!

[@ExamSolutions_Maths]

No probs.

[@hellahasarwari6220]

thanks for the it was very helpful

[@ExamSolutions_Maths]

That's ok. Cheers

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You rock!!!

[@MrMrgamerwatch]

Brilliant, only video I could find which actually brought me to a solution, thanks

[@JoeRoganCl1pz]

ayo

[@Vusi2020]

Great videos. Thanks. Quick question: How do I tackle a question like this: Equation of a curve is xy ^2 = 2x+3y, show that the curve has no tangent parallel to the y-axis. Thanking you in advance

[@HowOriginal03]

thanx, i will get good grades in Additional Mathematics :)

[@DilmiKarunadasa]

this was super helpful. thank you

[@ExamSolutions_Maths]

That's good. Thanks for watching.

[@troypie7020]

The video script explains how to find equations of tangents and normals to a general curve by using the gradient and coordinates of a point on the curve. It includes a numerical example of finding the equations of tangent and normal to y=x^2+1 at x=3. The script demonstrates the process step by step for better understanding. Key moments: 00:07 Understanding how to find equations of tangents and normals to a curve involves differentiating the curve to determine the gradient and substituting values to find specific points on the curve. -Tangents and normals. Tangents touch the curve at a point, while normals are perpendicular to tangents. Equations of both involve gradients and specific points on the curve. -Gradient calculation. Gradients for tangents and normals are determined by differentiating the curve with respect to X, and substituting values to find specific points. 05:10 Finding equations of tangent and normal lines involves using the point-slope form with given point and gradient, then converting to standard form for both lines. -Equation of tangent line. Use point-slope form Y - y1 = M(X - x1) with point (x1, y1) and gradient M to find the equation. -Equation of normal line. Similar process as tangent but with negative reciprocal gradient. Convert to standard form Ax + By + C = 0.

[@wysestgh4494]

Please can there a case where the values of X and Y are not given, can we use the intercept form to fine for the values of X and Y

[@theonlyone720]

Brilliant! Just a quick question, do we have to put the tangent in the form of y=mx+c and the normal in the form of ax+by+c=0? Or does it not matter which format you leave it in? Or will the question specify? cheers

[@mostafakamaly]

@ExamSolutions Have you got a video on the log rule?

[@donnellb9934]

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[@ExamSolutions_Maths]

You're welcome

[@ElephantGirl535]

Can you write the equation of the normal in the form y=mx+c or does it have to be in the form which is equal to zero?

[@ExamSolutions_Maths]

Yes

[@starshain]

@ExamSolutions hope so too. my maths teacher just can't explain especially in english (i'm from switzerland.)

[@glennrickelton4093]

At 8 minutes towards the end of your video when you had a gradient of - 1/6 (X - 3) you didn't multiply through the parentheses and simply multiplied the 6 over the other side of the equation. I assume this is because you would then have multiplied by 6 so the equation in the parentheses would have ended up the same. If the gradient was 2/3 then I am assuming it would have to be multiplied by the 2/3 as leaving the equation in the parentheses without multiplying would not give the same result

[@ExamSolutions_Maths]

No probs.

[@AnonymousAnonymous-pp5of]

Thank you so much

[@ExamSolutions_Maths]

That's okay. Thanks for watching and best wishes.

[@ExamSolutions_Maths]

Find dy/dx using implicit differentiation and check that the denominator cannot equal zero.

[@ExamSolutions_Maths]

goes to -1. The differential of ax where a is a constant is a

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[@ExamSolutions_Maths]

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[@24kmagic27]

Hi i dont get why straight lines form y-y1=m(x-x1) do u have a video explaining the reason why ? :(

[@shantanuthakur6081]

It is locus of line. We can represent a line using this equation. There are many ways to represent lines, just google it

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You might find, "Coordinate Geometry : Equation of a Line ( 2 ) : ExamSolutions, useful.

[@mahek3510]

Thanqu😁😁😘😘💞💞

[@ExamSolutions_Maths]

No problem. Thanks for watching.

[@ExamSolutions_Maths]

Solve them simultaneously

[@adirajuadithya]

@uploader.. help on how to fing length of tangent???

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living legend

[@adirajuadithya]

@ExamSolutions then what is a subtangent??

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[@ExamSolutions_Maths]

@mostafakamaly Pleasure - thank you for your comment

[@ExamSolutions_Maths]

Best wishes for tomorrow.

[@ExamSolutions_Maths]

The question usually specifies. If not then it is up to you.

[@ExamSolutions_Maths]

@adirajuadithya Thanks

[@ExamSolutions_Maths]

Cool

[@ExamSolutions_Maths]

@LostTime19 Thanks for your support

[@superlambmilkshake4904]

What’s the point of the last step? Just use the equation y=mx+b so it’s y=-1/6x+b and we know x=3 and y=10 so rearrange to get b so our final answer is y=-1/6x+21/2 which is exactly the answer u got. Instead I used a simple y=mx+b equation once I knew m equals negative reciprocal of the tangent at that point

[@ExamSolutions_Maths]

@starshain Cool - hope it goes well for you

[@ExamSolutions_Maths]

Hope you get that A!

[@dubtob]

what dose x^3-x+3 differentiate to? i know that it goes to 3x^2 and leave the +3 but what happens to the x ?!??!

[@ExamSolutions_Maths]

@3iMi5 yes

[@ExamSolutions_Maths]

@woundedtiger40 That's ok

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[@ExamSolutions_Maths]

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[@ExamSolutions_Maths]

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[@ExamSolutions_Maths]

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[@ExamSolutions_Maths]

That's okay. Pleased to hear it was useful.

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Nope

[@HowOriginal03]

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[@ExamSolutions_Maths]

@HowOriginal03 Good luck

[@overlordnodder8076]

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[@JaZpInDeR]

@MrNaveed10 Integration is just differentiation backwards :) Not that difficult :) He hasn't got a tutorial up on it YET unfortunately :(

[@veenitmoosun766]

Euuh will I get the same answer I used

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[@ExamSolutions_Maths]

Best wishes

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[@iAmLauRawr]

I understood everything till i reached 7:44 -_-

[@ryangoburdhone8149]

sorry but how did you get 2x ?

[@odynamikhounor4597]

+Ryan Goburdhone 2x is the derivative of the function

[@rajchopra3868]

differentiation of x^n = n.x^n-1 here d/dx x^2 = 2x . : ]

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"Are the videos from 2006 really helping?".... Nigga it's not like the laws of mathematics change

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still don’t understand mEh