Derivatives of Exponential Functions & Logarithmic Differentiation Calculus lnx, e^2x, x^x, x^sinx

[@TheOrganicChemistryTutor]

Derivatives - Free Formula Sheet: bit.ly/4dThzf1 Final Exams and Video Playlists: www.video-tutor.net/ Calculus 1 Final Exam Review: kzbin.info/www/bejne/jZ6lq6B-p9pqbtk

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@@mohanranaeducationclasses3166 help me please at 27:18 i don't understand why he cancel the x on the top

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@@sanopann1896 It was to simplify the answer. Since there was a fraction in the numerator, he multiplied top and bottom by x to get rid of the fraction "1/x"

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big sis help me please at 27:18 i don't understand why he cancel the x on the top

[@nootnootimaboot8798]

@@sanopann1896 hey i hope you got help w this, but basically he wants to simplify it, & there's this thing with fractions where you can multiply the top and bottom by anything (as long as you multiply the same thing in the top and bottom, it doesn't change it at all. it's like multiplying by 1/1). so you can choose something to conveniently make the fraction easier to work with, like this. when you do [(1/x)*(x/1)] you end up with 1*x/x*1... simplifies to x/x, or 1 :) so then the whole problem is easier to manage

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big bro need help at 5:12 why it was ex^e-1 instead of ex

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​@sano pann because it's variable raised to a constant, the derivative of x^2 is 2x. The derivatives of 2^x is (2^x)(1)ln2

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Trigonometric Derivatives *Hope this helps!* d(ln (u)) = (1/u) (du/dx) d(log_a^u) = (1/ln a u) (du/dx) d(e^u) = e^u du/dx d(a^u) = ln a a^u (du/dx

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