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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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Frequently Asked Questions (FAQ)

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