What is the derivative of ((x+2/(x-2))^5) ?

The derivative of ((x+2/(x-2))^5) is -(20(x+2)^4)/((x-2)^6)

What is the first derivative of ((x+2/(x-2))^5) ?

The first derivative of ((x+2/(x-2))^5) is -(20(x+2)^4)/((x-2)^6)

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

- \frac{20 ( x + 2 ) ^{4}}{( x - 2 ) ^{6}}

Solution steps

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

Apply the chain rule:

5 (\frac{x + 2}{x - 2})^{4} \frac{d}{d x} (\frac{x + 2}{x - 2})

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

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

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

Simplify

5 (\frac{x + 2}{x - 2})^{4} (- \frac{4}{( x - 2 ) ^{2}}) : - \frac{20 ( x + 2 ) ^{4}}{( x - 2 ) ^{6}}

= - \frac{20 ( x + 2 ) ^{4}}{( x - 2 ) ^{6}}

\frac{d}{d x} (2 x^{2} + y^{2})

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

\frac{d y}{d x} = 3 x y

\int_{0}^{1} 14 cos (x^{2}) d x

\frac{2}{( s + 2 ) ( s + 3 )}

What is the derivative of ((x+2/(x-2))^5) ?
The derivative of ((x+2/(x-2))^5) is -(20(x+2)^4)/((x-2)^6)
What is the first derivative of ((x+2/(x-2))^5) ?
The first derivative of ((x+2/(x-2))^5) is -(20(x+2)^4)/((x-2)^6)