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

The derivative of (ln(sin^x(x))/x) is (x(ln(sin(x))+xcot(x))-ln(sin^x(x)))/(x^2)

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

The first derivative of (ln(sin^x(x))/x) is (x(ln(sin(x))+xcot(x))-ln(sin^x(x)))/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{x ( ln ( sin ( x ) ) + x cot ( x ) ) - ln ( sin ^{x} ( x ) )}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (ln (sin^{x} (x))) = ln (sin (x)) + x cot (x)

\frac{d x}{d x} = 1

= \frac{( ln ( sin ( x ) ) + x cot ( x ) ) x - 1 \cdot ln ( sin ^{x} ( x ) )}{x ^{2}}

Simplify

= \frac{x ( ln ( sin ( x ) ) + x cot ( x ) ) - ln ( sin ^{x} ( x ) )}{x ^{2}}

sin (7 x)

x^{3} - 2 x^{2} + 4, 3 x^{2} + 5 x - 21

\int_{0}^{60} 100 e^{- 0.01 x} d x

y = x e^{9 x}

\frac{1}{3} (x^{2} - 2)^{\frac{3}{2}}

What is the derivative of (ln(sin^x(x))/x) ?
The derivative of (ln(sin^x(x))/x) is (x(ln(sin(x))+xcot(x))-ln(sin^x(x)))/(x^2)
What is the first derivative of (ln(sin^x(x))/x) ?
The first derivative of (ln(sin^x(x))/x) is (x(ln(sin(x))+xcot(x))-ln(sin^x(x)))/(x^2)