What is (\partial)/(\partial x)(ln(sin^2(x))) ?

The answer to (\partial)/(\partial x)(ln(sin^2(x))) is 2cot(x)

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(\partial)/(\partial x)(ln(sin^2(x)))

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

2 cot (x)

Solution steps

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

Apply the chain rule:

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

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

\frac{\partial}{\partial 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)

n = 0 \sum \infty 2^{n} \cdot (\frac{1}{4})^{l n (2^{n})}

\frac{d ^{2} y}{d x ^{2}} = 4 e^{- x}, y (0) = 3, y^{^{'}} (0) = 2

\frac{1}{2 r} + \frac{1}{3 r ^{\frac{2}{3}}}

y \to \infty lim (\frac{1}{5} (2 y^{2} + 3 y) x)

2 - x^{2}, 10 - 6 x

What is (\partial)/(\partial x)(ln(sin^2(x))) ?
The answer to (\partial)/(\partial x)(ln(sin^2(x))) is 2cot(x)