What is the derivative of 1/((x+k^3)) ?

The derivative of 1/((x+k^3)) is -3/((x+k)^4)

What is the first derivative of 1/((x+k^3)) ?

The first derivative of 1/((x+k^3)) is -3/((x+k)^4)

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

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

Solution steps

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

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

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

\frac{d}{d x} (x + k) = 1

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

Simplify

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

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