What is the derivative of f(x)=ln(sin^2(x)) ?

The derivative of f(x)=ln(sin^2(x)) is 2cot(x)

What is the first derivative of f(x)=ln(sin^2(x)) ?

The first derivative of f(x)=ln(sin^2(x)) is 2cot(x)

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derivative

2 cot (x)

Solution steps

\frac{d}{d x} (ln (sin^{2} (x)))

Apply the chain rule:

\frac{1}{sin ^{2} ( x )} \frac{d}{d x} (sin^{2} (x))

= \frac{1}{sin ^{2} ( x )} \frac{d}{d x} (sin^{2} (x))

\frac{d}{d x} (sin^{2} (x)) = sin (2 x)

= \frac{1}{sin ^{2} ( x )} sin (2 x)

Simplify

\frac{1}{sin ^{2} ( x )} sin (2 x) : 2 cot (x)

= 2 cot (x)

What is the derivative of f(x)=ln(sin^2(x)) ?
The derivative of f(x)=ln(sin^2(x)) is 2cot(x)
What is the first derivative of f(x)=ln(sin^2(x)) ?
The first derivative of f(x)=ln(sin^2(x)) is 2cot(x)