What is the derivative of f(x)=ln(289sin^2(x)) ?

The derivative of f(x)=ln(289sin^2(x)) is 2cot(x)

What is the first derivative of f(x)=ln(289sin^2(x)) ?

The first derivative of f(x)=ln(289sin^2(x)) is 2cot(x)

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derivative of

f (x) = ln (289 sin^{2} (x))

2 cot (x)

Solution steps

\frac{d}{d x} (ln (289 sin^{2} (x)))

Apply the chain rule:

\frac{1}{289 sin ^{2} ( x )} \frac{d}{d x} (289 sin^{2} (x))

= \frac{1}{289 sin ^{2} ( x )} \frac{d}{d x} (289 sin^{2} (x))

\frac{d}{d x} (289 sin^{2} (x)) = 578 sin (x) cos (x)

= \frac{1}{289 sin ^{2} ( x )} \cdot 578 sin (x) cos (x)

Simplify

\frac{1}{289 sin ^{2} ( x )} \cdot 578 sin (x) cos (x) : 2 cot (x)

= 2 cot (x)

\frac{d}{d x} (2 x^{4} y - 4)

y^{^{''''}} - 16 y = 0

\frac{d}{d t} (2 t^{\frac{4}{3}} - 3 t^{\frac{2}{3}})

\frac{d}{d x} (3 e^{x} + \frac{4}{3 x})

e^{x} cos (2 x)

What is the derivative of f(x)=ln(289sin^2(x)) ?
The derivative of f(x)=ln(289sin^2(x)) is 2cot(x)
What is the first derivative of f(x)=ln(289sin^2(x)) ?
The first derivative of f(x)=ln(289sin^2(x)) is 2cot(x)