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)

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derivative of

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

\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}}

x \to 0 lim (ln (\frac{x}{1 - x}))

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

\int (e^{3 x} - 2)^{2} d x

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

\int x^{2} + 3 x - 2 d x

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)