What is the derivative of ((x-7/(x+2))^3) ?

The derivative of ((x-7/(x+2))^3) is (27(x-7)^2)/((x+2)^4)

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

The first derivative of ((x-7/(x+2))^3) is (27(x-7)^2)/((x+2)^4)

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

\frac{27 ( x - 7 ) ^{2}}{( x + 2 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x - 7}{x + 2}) = \frac{9}{( x + 2 ) ^{2}}

= 3 (\frac{x - 7}{x + 2})^{2} \frac{9}{( x + 2 ) ^{2}}

Simplify

3 (\frac{x - 7}{x + 2})^{2} \frac{9}{( x + 2 ) ^{2}} : \frac{27 ( x - 7 ) ^{2}}{( x + 2 ) ^{4}}

= \frac{27 ( x - 7 ) ^{2}}{( x + 2 ) ^{4}}

y = \frac{8 - x e ^{x}}{x + e ^{x}}

\frac{\partial}{\partial x} (\frac{2 F ( V , x , P )}{V ^{2} x P})

\frac{d ^{3}}{d x ^{3}} (\frac{5}{x})

y = (3 x^{6} - 2 x^{4})^{4}

What is the derivative of ((x-7/(x+2))^3) ?
The derivative of ((x-7/(x+2))^3) is (27(x-7)^2)/((x+2)^4)
What is the first derivative of ((x-7/(x+2))^3) ?
The first derivative of ((x-7/(x+2))^3) is (27(x-7)^2)/((x+2)^4)