What is the derivative of ln(9sin^2(x)) ?

The derivative of ln(9sin^2(x)) is 2cot(x)

What is the first derivative of ln(9sin^2(x)) ?

The first derivative of ln(9sin^2(x)) is 2cot(x)

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derivative of

ln (9 sin^{2} (x))

2 cot (x)

Solution steps

\frac{d}{d x} (ln (9 sin^{2} (x)))

Apply the chain rule:

\frac{1}{9 sin ^{2} ( x )} \frac{d}{d x} (9 sin^{2} (x))

= \frac{1}{9 sin ^{2} ( x )} \frac{d}{d x} (9 sin^{2} (x))

\frac{d}{d x} (9 sin^{2} (x)) = 9 sin (2 x)

= \frac{1}{9 sin ^{2} ( x )} \cdot 9 sin (2 x)

Simplify

\frac{1}{9 sin ^{2} ( x )} \cdot 9 sin (2 x) : 2 cot (x)

= 2 cot (x)

\frac{d}{d u} (\frac{5 u}{4 u ^{2} + 1})

y = \frac{1}{x}, at x = 2

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 8 y ^{2}})

\int \frac{1}{ln ( x + 1 )} d x

\int \frac{1}{x ^{2} 10 x + 1} d x

What is the derivative of ln(9sin^2(x)) ?
The derivative of ln(9sin^2(x)) is 2cot(x)
What is the first derivative of ln(9sin^2(x)) ?
The first derivative of ln(9sin^2(x)) is 2cot(x)