What is the derivative of 1/((x+2)^4) ?

The derivative of 1/((x+2)^4) is -4/((x+2)^5)

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

The first derivative of 1/((x+2)^4) is -4/((x+2)^5)

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derivative

- \frac{4}{( x + 2 ) ^{5}}

Solution steps

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

Apply exponent rule:

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

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

Apply the chain rule:

- \frac{4}{( x + 2 ) ^{5}} \frac{d}{d x} (x + 2)

= - \frac{4}{( x + 2 ) ^{5}} \frac{d}{d x} (x + 2)

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

= - \frac{4}{( x + 2 ) ^{5}} \cdot 1

Simplify

= - \frac{4}{( x + 2 ) ^{5}}

What is the derivative of 1/((x+2)^4) ?
The derivative of 1/((x+2)^4) is -4/((x+2)^5)
What is the first derivative of 1/((x+2)^4) ?
The first derivative of 1/((x+2)^4) is -4/((x+2)^5)