en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x^4+3x)^{-1}

Solution

derivative of

(x^{4} + 3 x)^{- 1}

Solution

- \frac{4 x ^{3} + 3}{( x ^{4} + 3 x ) ^{2}}

Solution steps

\frac{d}{d x} ((x^{4} + 3 x)^{- 1})

Apply the chain rule:

- \frac{1}{( x ^{4} + 3 x ) ^{2}} \frac{d}{d x} (x^{4} + 3 x)

= - \frac{1}{( x ^{4} + 3 x ) ^{2}} \frac{d}{d x} (x^{4} + 3 x)

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

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

Simplify

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

= - \frac{4 x ^{3} + 3}{( x ^{4} + 3 x ) ^{2}}

Popular Examples

integral from 0 to pi/2 of 1

\int_{0}^{\frac{π}{2}} 1 d θ

derivative of x^2+(3456/x)

\frac{d}{d x} (x^{2} + \frac{3456}{x})

inverse oflaplace 1/(s(s^2+81))inverse laplace

\frac{1}{s ( s ^{2} + 81 )}

d/(dy)(sqrt((w(x+y))/(xy)))

\frac{d}{d y} (\frac{w ( x + y )}{x y})

integral from 1 to 4 of (x^2+4)/(5x-x^2)

\int_{1}^{4} \frac{x ^{2} + 4}{5 x - x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^4+3x)^{-1} ?
The derivative of (x^4+3x)^{-1} is -(4x^3+3)/((x^4+3x)^2)
What is the first derivative of (x^4+3x)^{-1} ?
The first derivative of (x^4+3x)^{-1} is -(4x^3+3)/((x^4+3x)^2)