What is the derivative of ln(4sin^2(x)) ?

The derivative of ln(4sin^2(x)) is 2cot(x)

What is the first derivative of ln(4sin^2(x)) ?

The first derivative of ln(4sin^2(x)) is 2cot(x)

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\frac{d}{d x} (ln (4 sin^{2} (x)))

2 cot (x)

Solution steps

\frac{d}{d x} (ln (4 sin^{2} (x)))

Apply the chain rule:

\frac{1}{4 sin ^{2} ( x )} \frac{d}{d x} (4 sin^{2} (x))

= \frac{1}{4 sin ^{2} ( x )} \frac{d}{d x} (4 sin^{2} (x))

\frac{d}{d x} (4 sin^{2} (x)) = 4 sin (2 x)

= \frac{1}{4 sin ^{2} ( x )} \cdot 4 sin (2 x)

Simplify

\frac{1}{4 sin ^{2} ( x )} \cdot 4 sin (2 x) : 2 cot (x)

= 2 cot (x)

\frac{d}{d x} (3^{x} - 2^{x})

\frac{d}{d x} (x 6 - x^{2})

\int - 2 sin (t) d t

n = 2 \sum \infty \frac{7}{2 ^{n}}

\int_{0}^{1} \frac{32}{x ^{2} - 64} d x

What is the derivative of ln(4sin^2(x)) ?
The derivative of ln(4sin^2(x)) is 2cot(x)
What is the first derivative of ln(4sin^2(x)) ?
The first derivative of ln(4sin^2(x)) is 2cot(x)