What is the derivative of f(x)=(x^4+3x)^{-1} ?

The derivative of f(x)=(x^4+3x)^{-1} is -(4x^3+3)/((x^4+3x)^2)

What is the first derivative of f(x)=(x^4+3x)^{-1} ?

The first derivative of f(x)=(x^4+3x)^{-1} is -(4x^3+3)/((x^4+3x)^2)

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derivative of

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

- \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}}

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