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

The derivative of ((x+3)/(x-2))^3 is -(15(x+3)^2)/((x-2)^4)

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

The first derivative of ((x+3)/(x-2))^3 is -(15(x+3)^2)/((x-2)^4)

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derivative of

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

- \frac{15 ( x + 3 ) ^{2}}{( x - 2 ) ^{4}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x + 3}{x - 2}) = - \frac{5}{( x - 2 ) ^{2}}

= 3 (\frac{x + 3}{x - 2})^{2} (- \frac{5}{( x - 2 ) ^{2}})

Simplify

3 (\frac{x + 3}{x - 2})^{2} (- \frac{5}{( x - 2 ) ^{2}}) : - \frac{15 ( x + 3 ) ^{2}}{( x - 2 ) ^{4}}

= - \frac{15 ( x + 3 ) ^{2}}{( x - 2 ) ^{4}}

What is the derivative of ((x+3)/(x-2))^3 ?
The derivative of ((x+3)/(x-2))^3 is -(15(x+3)^2)/((x-2)^4)
What is the first derivative of ((x+3)/(x-2))^3 ?
The first derivative of ((x+3)/(x-2))^3 is -(15(x+3)^2)/((x-2)^4)