Derivative of log x with any Base Explained | Calculus 1

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We show the derivative of loga(x) is 1/(xlna) using implicit differentiation, our formula for the derivative of an exponential function a^x, and the chain rule! Then we plug in a=e to see the derivative of lnx is 1/x. We also find the derivative of log_3x using our new formula. #calculus1 #calculus

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Another way to find the derivative of y=log_a(x) is to use the change of base formula in terms of ln(x). y=log_a(x)=ln(x)/ln(a). Therefore, we know that the derivative of ln(x) is 1/x. Multiply that by 1/ln(a), which is 1/(xln(a)). Therefore, y'=1/(xln(a)).

justabunga

Thank you so much, great explanation!

bradocksolo

awesome. very good explanation. thank you.

vil

Derivative of log x with any Base Explained | Calculus 1

Derivative of log x with any Base Explained | Calculus 1

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