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Differentiate the function.

$ f(x) = \ln (\sin^2 x) $

2 $\cot x$

00:32

Frank L.

00:47

Doruk I.

01:15

Carson M.

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions

Derivatives

Differentiation

Baylor University

University of Michigan - Ann Arbor

Boston College

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

00:28

Differentiate the function…

00:23

00:39

01:23

Differentiate.

$ …

00:34

Find the derivative of the…

00:33

01:22

00:59

00:55

Differentiate.$f(x)=\s…

So we want to find the derivative of Ellen of Science square X. Now recall that the derivative of Ellen of any function is, so the function is F. Of X. So it's F. Prime over F. So when finding the derivative of Ellen of Science square X. It's going to be derivative of sine square X. Divided by sine square X. Now to find the derivative of sine squared X. We look at this formula derivative of a function G of X rays to the R is R times G of X rays to the R minus one times the derivative of G of X. So the derivative of sine square X, which is same as the derivative of sin X squared. So using this formula above, it's going to be Two times Synnex raised the 2 -1 times the derivative of Sin X. Which we know is cosine X. So the derivative of Sine square X is two times Sine X times cosine X. So we replace that here we get two times Sin X times Cosine X divided by sine squared X. So from the numerator and denominator we can cancel out a factor of sin X. And so we get two times cosign X divided by Synnex. And we know that psycho sign over Sinus co tangent. So two times got x.

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