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Popular >

derivative of 4/((x+2^3))

Solution

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

Solution

- \frac{12}{( x + 2 ) ^{4}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

4 (- \frac{3}{( x + 2 ) ^{4}} \cdot 1) : - \frac{12}{( x + 2 ) ^{4}}

= - \frac{12}{( x + 2 ) ^{4}}

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Frequently Asked Questions (FAQ)

What is the derivative of 4/((x+2^3)) ?
The derivative of 4/((x+2^3)) is -(12)/((x+2)^4)
What is the first derivative of 4/((x+2^3)) ?
The first derivative of 4/((x+2^3)) is -(12)/((x+2)^4)