What is the derivative of 1/((x^2+8)^5) ?

The derivative of 1/((x^2+8)^5) is -(10x)/((x^2+8)^6)

What is the first derivative of 1/((x^2+8)^5) ?

The first derivative of 1/((x^2+8)^5) is -(10x)/((x^2+8)^6)

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derivative of

\frac{1}{( x ^{2} + 8 ) ^{5}}

- \frac{10 x}{( x ^{2} + 8 ) ^{6}}

Solution steps

\frac{d}{d x} (\frac{1}{( x ^{2} + 8 ) ^{5}})

Apply exponent rule:

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

= \frac{d}{d x} ((x^{2} + 8)^{- 5})

Apply the chain rule:

- \frac{5}{( x ^{2} + 8 ) ^{6}} \frac{d}{d x} (x^{2} + 8)

= - \frac{5}{( x ^{2} + 8 ) ^{6}} \frac{d}{d x} (x^{2} + 8)

\frac{d}{d x} (x^{2} + 8) = 2 x

= - \frac{5}{( x ^{2} + 8 ) ^{6}} \cdot 2 x

Simplify

- \frac{5}{( x ^{2} + 8 ) ^{6}} \cdot 2 x : - \frac{10 x}{( x ^{2} + 8 ) ^{6}}

= - \frac{10 x}{( x ^{2} + 8 ) ^{6}}

What is the derivative of 1/((x^2+8)^5) ?
The derivative of 1/((x^2+8)^5) is -(10x)/((x^2+8)^6)
What is the first derivative of 1/((x^2+8)^5) ?
The first derivative of 1/((x^2+8)^5) is -(10x)/((x^2+8)^6)