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Popular >

derivative of ((x-6/(x+7))^3)

Solution

\frac{d}{d x} ((\frac{x - 6}{x + 7})^{3})

Solution

\frac{39 ( x - 6 ) ^{2}}{( x + 7 ) ^{4}}

Solution steps

\frac{d}{d x} ((\frac{x - 6}{x + 7})^{3})

Apply the chain rule:

3 (\frac{x - 6}{x + 7})^{2} \frac{d}{d x} (\frac{x - 6}{x + 7})

= 3 (\frac{x - 6}{x + 7})^{2} \frac{d}{d x} (\frac{x - 6}{x + 7})

\frac{d}{d x} (\frac{x - 6}{x + 7}) = \frac{13}{( x + 7 ) ^{2}}

= 3 (\frac{x - 6}{x + 7})^{2} \frac{13}{( x + 7 ) ^{2}}

Simplify

3 (\frac{x - 6}{x + 7})^{2} \frac{13}{( x + 7 ) ^{2}} : \frac{39 ( x - 6 ) ^{2}}{( x + 7 ) ^{4}}

= \frac{39 ( x - 6 ) ^{2}}{( x + 7 ) ^{4}}

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Frequently Asked Questions (FAQ)

What is the derivative of ((x-6/(x+7))^3) ?
The derivative of ((x-6/(x+7))^3) is (39(x-6)^2)/((x+7)^4)
What is the first derivative of ((x-6/(x+7))^3) ?
The first derivative of ((x-6/(x+7))^3) is (39(x-6)^2)/((x+7)^4)