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Popular >

derivative of ln(144sin^2(x))

Solution

derivative of

ln (144 sin^{2} (x))

Solution

2 cot (x)

Solution steps

\frac{d}{d x} (ln (144 sin^{2} (x)))

Apply the chain rule:

\frac{1}{144 sin ^{2} ( x )} \frac{d}{d x} (144 sin^{2} (x))

= \frac{1}{144 sin ^{2} ( x )} \frac{d}{d x} (144 sin^{2} (x))

\frac{d}{d x} (144 sin^{2} (x)) = 288 sin (x) cos (x)

= \frac{1}{144 sin ^{2} ( x )} \cdot 288 sin (x) cos (x)

Simplify

\frac{1}{144 sin ^{2} ( x )} \cdot 288 sin (x) cos (x) : 2 cot (x)

= 2 cot (x)

Popular Examples

integral from 8 to 10 of x

\int_{8}^{10} x d x

integral from 1 to e of ln(19x)

\int_{1}^{e} ln (19 x) d x

limit as x approaches 8+of 1/(x+8)

x \to 8 + lim (\frac{1}{x + 8})

(\partial)/(\partial x)(xln(z^2+x^2))

\frac{\partial}{\partial x} (x ln (z^{2} + x^{2}))

derivative of (x^2+2(x^4+1))

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

Frequently Asked Questions (FAQ)

What is the derivative of ln(144sin^2(x)) ?
The derivative of ln(144sin^2(x)) is 2cot(x)
What is the first derivative of ln(144sin^2(x)) ?
The first derivative of ln(144sin^2(x)) is 2cot(x)