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Popular >

derivative of (1+7/x ^5)

Solution

\frac{d}{d x} ((1 + \frac{7}{x})^{5})

Solution

- \frac{35 ( x + 7 ) ^{4}}{x ^{6}}

Solution steps

\frac{d}{d x} ((1 + \frac{7}{x})^{5})

Apply the chain rule:

5 (1 + \frac{7}{x})^{4} \frac{d}{d x} (1 + \frac{7}{x})

= 5 (1 + \frac{7}{x})^{4} \frac{d}{d x} (1 + \frac{7}{x})

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

= 5 (1 + \frac{7}{x})^{4} (- \frac{7}{x ^{2}})

Simplify

5 (1 + \frac{7}{x})^{4} (- \frac{7}{x ^{2}}) : - \frac{35 ( x + 7 ) ^{4}}{x ^{6}}

= - \frac{35 ( x + 7 ) ^{4}}{x ^{6}}

Graph

Popular Examples

derivative of y=ln(sqrt(x^2-9))derivative of

y = ln (x^{2} - 9)

limit as x approaches-3 of sqrt(5x^2+2x)

x \to - 3 lim (5 x^{2} + 2 x)

integral of (1+x)/(1-\sqrt[3]{x)}

\int \frac{1 + x}{1 - 3 x} d x

limit as x approaches 3 of (x-2)/(x-3)

x \to 3 lim (\frac{x - 2}{x - 3})

integral of 3/(4(4-3x)^7)

\int \frac{3}{4 ( 4 - 3 x ) ^{7}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (1+7/x ^5) ?
The derivative of (1+7/x ^5) is -(35(x+7)^4)/(x^6)
What is the first derivative of (1+7/x ^5) ?
The first derivative of (1+7/x ^5) is -(35(x+7)^4)/(x^6)