en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arctan(sin(8x))

Solution

\frac{d}{d x} (arctan (sin (8 x)))

Solution

\frac{8 cos ( 8 x )}{sin ^{2} ( 8 x ) + 1}

Solution steps

\frac{d}{d x} (arctan (sin (8 x)))

Apply the chain rule:

\frac{1}{( sin ( 8 x ) ) ^{2} + 1} \frac{d}{d x} (sin (8 x))

= \frac{1}{( sin ( 8 x ) ) ^{2} + 1} \frac{d}{d x} (sin (8 x))

\frac{d}{d x} (sin (8 x)) = cos (8 x) \cdot 8

= \frac{1}{( sin ( 8 x ) ) ^{2} + 1} cos (8 x) \cdot 8

Simplify

\frac{1}{sin ^{2} ( 8 x ) + 1} cos (8 x) \cdot 8 : \frac{8 cos ( 8 x )}{sin ^{2} ( 8 x ) + 1}

= \frac{8 cos ( 8 x )}{sin ^{2} ( 8 x ) + 1}

Graph

Popular Examples

integral of (sin^3(x))/(cos^2(x))

\int \frac{sin ^{3} ( x )}{cos ^{2} ( x )} d x

tangent of f(x)=2-xe^x,\at x=0 tangent of

f (x) = 2 - x e^{x}, at x = 0

y^'=e^{-y}(2x-4),y(0)=1

y^{^{'}} = e^{- y} (2 x - 4), y (0) = 1

y^{''}+6y^'+9y=4e^{-3t}

y^{^{''}} + 6 y^{^{'}} + 9 y = 4 e^{- 3 t}

y=ln(x^3e^{2x})

y = ln (x^{3} e^{2 x})

Frequently Asked Questions (FAQ)

What is the derivative of arctan(sin(8x)) ?
The derivative of arctan(sin(8x)) is (8cos(8x))/(sin^2(8x)+1)
What is the first derivative of arctan(sin(8x)) ?
The first derivative of arctan(sin(8x)) is (8cos(8x))/(sin^2(8x)+1)