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Popular >

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

Solution

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

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

limit as x approaches+0-of arctan(1/x)

x \to + 0 - lim (arctan (\frac{1}{x}))

simplify (-a)/(x^2)+a/((x-2)^2)simplify

\frac{- a}{x ^{2}} + \frac{a}{( x - 2 ) ^{2}}

derivative of f(x)=(2x+3)/(x^2+3x+15)derivative of

f (x) = \frac{2 x + 3}{x ^{2} + 3 x + 15}

integral from 0 to 2 of 1/(4-2x)

\int_{0}^{2} \frac{1}{4 - 2 x} 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)