en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (1+sin(x))^{-4}

Solution

derivative of

(1 + sin (x))^{- 4}

Solution

- \frac{4 cos ( x )}{( 1 + sin ( x ) ) ^{5}}

Solution steps

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

Apply the chain rule:

- \frac{4}{( 1 + sin ( x ) ) ^{5}} \frac{d}{d x} (1 + sin (x))

= - \frac{4}{( 1 + sin ( x ) ) ^{5}} \frac{d}{d x} (1 + sin (x))

\frac{d}{d x} (1 + sin (x)) = cos (x)

= - \frac{4}{( 1 + sin ( x ) ) ^{5}} cos (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= - \frac{4 cos ( x )}{( 1 + sin ( x ) ) ^{5}}

Popular Examples

integral of (1/x+1/(3-x))

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

limit as x approaches 0 of sin(5x)csc(3x)

x \to 0 lim (sin (5 x) csc (3 x))

laplacetransform 0.02(1+3cos(t))laplace transform

0.02 (1 + 3 cos (t))

(dy)/(dt)=25-10t-2y

\frac{d y}{d t} = 25 - 10 t - 2 y

area 2(x+1),3(x+1),x=3 area

2 (x + 1), 3 (x + 1), x = 3

Frequently Asked Questions (FAQ)

What is the derivative of (1+sin(x))^{-4} ?
The derivative of (1+sin(x))^{-4} is -(4cos(x))/((1+sin(x))^5)
What is the first derivative of (1+sin(x))^{-4} ?
The first derivative of (1+sin(x))^{-4} is -(4cos(x))/((1+sin(x))^5)