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derivative of 1/12 (x+2^3+(x+2)^{-1})

Solution

\frac{d}{d x} (\frac{1}{12} (x + 2)^{3} + (x + 2)^{- 1})

Solution

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

Solution steps

\frac{d}{d x} (\frac{1}{12} (x + 2)^{3} + (x + 2)^{- 1})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{12} (x + 2)^{3}) + \frac{d}{d x} ((x + 2)^{- 1})

\frac{d}{d x} (\frac{1}{12} (x + 2)^{3}) = \frac{( x + 2 ) ^{2}}{4}

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

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

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Frequently Asked Questions (FAQ)

What is the derivative of 1/12 (x+2^3+(x+2)^{-1}) ?
The derivative of 1/12 (x+2^3+(x+2)^{-1}) is ((x+2)^2)/4-1/((x+2)^2)
What is the first derivative of 1/12 (x+2^3+(x+2)^{-1}) ?
The first derivative of 1/12 (x+2^3+(x+2)^{-1}) is ((x+2)^2)/4-1/((x+2)^2)