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Popular >

derivative of (x+2^4-(x+2)^{-2})

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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