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Popular >

derivative of ln(16sin^2(x))

Solution

derivative of

ln (16 sin^{2} (x))

Solution

2 cot (x)

Solution steps

\frac{d}{d x} (ln (16 sin^{2} (x)))

Apply the chain rule:

\frac{1}{16 sin ^{2} ( x )} \frac{d}{d x} (16 sin^{2} (x))

= \frac{1}{16 sin ^{2} ( x )} \frac{d}{d x} (16 sin^{2} (x))

\frac{d}{d x} (16 sin^{2} (x)) = 32 sin (x) cos (x)

= \frac{1}{16 sin ^{2} ( x )} \cdot 32 sin (x) cos (x)

Simplify

\frac{1}{16 sin ^{2} ( x )} \cdot 32 sin (x) cos (x) : 2 cot (x)

= 2 cot (x)

Popular Examples

limit as x approaches 7+of 1/((x-7)^2)

x \to 7 + lim (\frac{1}{( x - 7 ) ^{2}})

derivative of (9x^2)/(sqrt(6+x^3))derivative of

\frac{9 x ^{2}}{6 + x ^{3}}

integral of 1/(xsqrt(-1+x^2))

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

integral from 2 to 4 of 4x

\int_{2}^{4} 4 x d x

limit as x approaches (5pi)/2+of sec(x)

x \to \frac{5 π}{2} + lim (sec (x))

Frequently Asked Questions (FAQ)

What is the derivative of ln(16sin^2(x)) ?
The derivative of ln(16sin^2(x)) is 2cot(x)
What is the first derivative of ln(16sin^2(x)) ?
The first derivative of ln(16sin^2(x)) is 2cot(x)