en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of arctan(2x^4)

Solution

\frac{d}{d x} (arctan (2 x^{4}))

Solution

\frac{8 x ^{3}}{4 x ^{8} + 1}

Solution steps

\frac{d}{d x} (arctan (2 x^{4}))

Apply the chain rule:

\frac{1}{( 2 x ^{4} ) ^{2} + 1} \frac{d}{d x} (2 x^{4})

= \frac{1}{( 2 x ^{4} ) ^{2} + 1} \frac{d}{d x} (2 x^{4})

\frac{d}{d x} (2 x^{4}) = 8 x^{3}

= \frac{1}{( 2 x ^{4} ) ^{2} + 1} \cdot 8 x^{3}

Simplify

\frac{1}{( 2 x ^{4} ) ^{2} + 1} \cdot 8 x^{3} : \frac{8 x ^{3}}{4 x ^{8} + 1}

= \frac{8 x ^{3}}{4 x ^{8} + 1}

Popular Examples

integral of (x^2+3)^42x

\int (x^{2} + 3)^{4} 2 x d x

integral of e^{-ax^2}

\int e^{- a x^{2}} d x

derivative of y=2\sqrt[3]{x}derivative of

tangent of y=(1+4x)^{11},(0,1)tangent of

y = (1 + 4 x)^{11}, (0, 1)

tangent of f(x)=(sqrt(x))/(x+6),\at x=4 tangent of

f (x) = \frac{x}{x + 6}, at x = 4

Frequently Asked Questions (FAQ)

What is the derivative of arctan(2x^4) ?
The derivative of arctan(2x^4) is (8x^3)/(4x^8+1)
What is the first derivative of arctan(2x^4) ?
The first derivative of arctan(2x^4) is (8x^3)/(4x^8+1)