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Popular >

derivative of (1+(10)/x)^8

Solution

derivative of

(1 + \frac{10}{x})^{8}

Solution

- \frac{80 ( x + 10 ) ^{7}}{x ^{9}}

Solution steps

\frac{d}{d x} ((1 + \frac{10}{x})^{8})

Apply the chain rule:

8 (1 + \frac{10}{x})^{7} \frac{d}{d x} (1 + \frac{10}{x})

= 8 (1 + \frac{10}{x})^{7} \frac{d}{d x} (1 + \frac{10}{x})

\frac{d}{d x} (1 + \frac{10}{x}) = - \frac{10}{x ^{2}}

= 8 (1 + \frac{10}{x})^{7} (- \frac{10}{x ^{2}})

Simplify

8 (1 + \frac{10}{x})^{7} (- \frac{10}{x ^{2}}) : - \frac{80 ( x + 10 ) ^{7}}{x ^{9}}

= - \frac{80 ( x + 10 ) ^{7}}{x ^{9}}

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Frequently Asked Questions (FAQ)

What is the derivative of (1+(10)/x)^8 ?
The derivative of (1+(10)/x)^8 is -(80(x+10)^7)/(x^9)
What is the first derivative of (1+(10)/x)^8 ?
The first derivative of (1+(10)/x)^8 is -(80(x+10)^7)/(x^9)