Derivative of sin(x^2), sin^2(x), and sin(2x) with Chain Rule | Calculus 1 Exercises

We find the derivative of sinx^2 with the chain rule, sin^2x with the chain rule, and sin2x also with the chain rule. Just for kicks, we also differentiate sin^2lnx at the end. #apcalculus #calculus1
Derivative of cos(x^2), cos^2(x), and cos(2x) with Chain Rule: • Derivative of cos(x^2)...
Derivative of tan(x^2), tan^2(x), and tan(2x) with Chain Rule: • Derivative of tan(x^2)...
Derivative of e^x^2, e^2x, and e^sinx with Chain Rule; • Derivative of e^2x, e^...
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[@WrathofMath]

The ULTIMATE Calculus Christmas Present: kzbin.info/www/bejne/pmLWanarm7OLbJI

[@neroslogic101]

Thank you, it was so hard to find someone who explained sin^2(x). and what rule to apply, how and why. There is something just strange about this format and how its actually done. Contrasting it against similar examples really hits the ball out the park.

[@TheStalkingEmu]

This video is really great at explaining this. I really needed this refresher since I just started calculus 2. Thanks a lot!

[@punditgi]

Calculus unchained with the Wrath of Math! 😃

[@billk8579]

Excellent explanation. Your video is very easy to understand an otherwise confusing problem.

[@WrathofMath]

Glad it helped, thanks for watching!

[@sado9961]

You are a legend

[@ishuyadav9330]

Cleared my all doubts . Tysm dude ❤❤❤

[@WrathofMath]

Happy to help! Check out my calc 1 exercises playlist for a whole lot more: kzbin.info/aero/PLztBpqftvzxUEqGGgvL3EuIQUNcAdmVhx

[@jayspice4987]

You explained it so easily. Bravo.

[@WrathofMath]

Thanks for watching!

[@deathless7_JSRBSKK]

Thanks sir ...

[@dolando5837]

Thank you this helped better than my professors explanation.

[@ayushverm9195]

thx bud love from india

[@WrathofMath]

Thanks for watching!

[@RouzaZidnee-nt5dp]

Thanks a lot❤

[@WrathofMath]

Glad to help! If you ever find yourself in need of say, 10 more hours of calc review, I've got you covered: kzbin.info/www/bejne/hYjLZ41_qNSjb68

[@keep-growing694]

Thanks a lots... you really explained very easily 😊

[@WrathofMath]

Glad it was helpful!

[@pragyapandey2841]

Thank u so much sir 💖 Please do make other vedios like this also 🔥

[@WrathofMath]

Thanks for watching! I have several others like this for other trig functions, and am working on more!

[@user-ox6oy7zf1q]

thank you ^^

[@WrathofMath]

No problem!

[@Benzene42]

Solve these with first principal method

[@Saikumar-cf6ql]

Thanks sir

[@WrathofMath]

Welcome!

[@user-yp9cw5eq3b]

Okay so I've understood everything else but how for (sin^2)x it is sin^2 that is the inside function not x

[@WrathofMath]

Thanks for watching and the question! sin^2 is not the inside function. We have f(x) = x^2 is the outside function and g(x) = sin(x) is the inside function. Our function then is f( g(x) ) = ( sin(x) )^2

[@harikrishna8146]

In the 3rd question, why is sin² an inside function bcz its clearly outside the bracket I really dont know anything, smone please help

[@thephoenix2598]

Thanks 😃😄

[@WrathofMath]

Glad to help!

[@pahadivloger8101]

Tq

[@WrathofMath]

Welcome!

[@davidgao6511]

thank you, i understood it in a second

[@WrathofMath]

Awesome, thanks for watching!

[@Ayush-kx8pm]

Hey guys , I m from europe I wanted to know what age group of students does it target basically at what age students learn this integration in your country

[@vloggerpogger1735]

What will the double derivative of sin^2(x) be?

[@WrathofMath]

Thanks for watching and for the question, you just use the product rule. The first derivative gives us 2sinx*cosx. Then say f(x)=2sinx and g(x)=cosx. So by the product rule, the second derivative, f' g + g' f will be 2cosx*cosx + (-sinx)*2sinx = 2cos^2x - 2sin^2x = 2cos2x.

[@vloggerpogger1735]

@@WrathofMath thanks

[@melihaktan2000]

what about (sinx)^2 😅 it always confusing my mind. Is it same with "sin^2(x)" ? 🤔

[@snowprincess4255]

Yes . Both of them indicates the same meaning. (Sinx)^2 = 2 sinx . Cosx (Sin^2)x = 2 sinx . Cosx

[@melihaktan2000]

@@snowprincess4255 thank u so much :)

[@The_boy_fvckin_up_SETs]

❤❤❤

[@WrathofMath]

Thanks for watching!

[@angusriffraff]

Does the chain rule also apply to d/dx sin(x)? i.e., d/dx sin(x) = cos(x)(1) = cos(x)

[@davidnssien3646]

What is the square of sin2x

[@WrathofMath]

(sin(2x))^2

[@davidnssien3646]

@@WrathofMath yeah, how do you expand it?

[@Benzene42]

Broo is in the evening

[@bbrfbe-c2512]

f(x)= sin^2 (2x)????

[@WrathofMath]

Two applications of the chain rule. Take the derivative like we did of sin^2(x). But keep a 2x in the sine, and then at the end multiply by 2 as that's the derivative of 2x.

[@bbrfbe-c2512]

@@WrathofMath thanks 😊 🙏

[@numbnation_zm2017]

So is the answer 2Sin2x•Cos2•2 Rewriting it ...4Sin2x*Cos2