en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=ln(81sin^2(x))

Solution

derivative of

f (x) = ln (81 sin^{2} (x))

Solution

2 cot (x)

Solution steps

\frac{d}{d x} (ln (81 sin^{2} (x)))

Apply the chain rule:

\frac{1}{81 sin ^{2} ( x )} \frac{d}{d x} (81 sin^{2} (x))

= \frac{1}{81 sin ^{2} ( x )} \frac{d}{d x} (81 sin^{2} (x))

\frac{d}{d x} (81 sin^{2} (x)) = 162 sin (x) cos (x)

= \frac{1}{81 sin ^{2} ( x )} \cdot 162 sin (x) cos (x)

Simplify

\frac{1}{81 sin ^{2} ( x )} \cdot 162 sin (x) cos (x) : 2 cot (x)

= 2 cot (x)

Popular Examples

derivative of (2x+1/(3x-2))

\frac{d}{d x} (\frac{2 x + 1}{3 x - 2})

limit as x approaches 3 of (x-3)/(x-2)

x \to 3 lim (\frac{x - 3}{x - 2})

tangent of y=7x-x^2,(1,6)tangent of

y = 7 x - x^{2}, (1, 6)

integral from 1 to 2 of x^4+2x^2

\int_{1}^{2} x^{4} + 2 x^{2} d x

integral from 0 to 1 of 5e^x-5xe^{x^2}

\int_{0}^{1} 5 e^{x} - 5 x e^{x^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=ln(81sin^2(x)) ?
The derivative of f(x)=ln(81sin^2(x)) is 2cot(x)
What is the first derivative of f(x)=ln(81sin^2(x)) ?
The first derivative of f(x)=ln(81sin^2(x)) is 2cot(x)