What is the derivative of ((x+3)/(x-3))^5 ?

The derivative of ((x+3)/(x-3))^5 is -(30(x+3)^4)/((x-3)^6)

What is the first derivative of ((x+3)/(x-3))^5 ?

The first derivative of ((x+3)/(x-3))^5 is -(30(x+3)^4)/((x-3)^6)

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derivative of

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

- \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

Solution steps

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

Apply the chain rule:

5 (\frac{x + 3}{x - 3})^{4} \frac{d}{d x} (\frac{x + 3}{x - 3})

= 5 (\frac{x + 3}{x - 3})^{4} \frac{d}{d x} (\frac{x + 3}{x - 3})

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

= 5 (\frac{x + 3}{x - 3})^{4} (- \frac{6}{( x - 3 ) ^{2}})

Simplify

5 (\frac{x + 3}{x - 3})^{4} (- \frac{6}{( x - 3 ) ^{2}}) : - \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

= - \frac{30 ( x + 3 ) ^{4}}{( x - 3 ) ^{6}}

\int 5 x 1 - x^{2} d x

\frac{d}{d x} (\frac{3 x + 2}{x + 1})

\int_{0}^{1} 8^{x} d x

\int \frac{1}{1 - 3 x ^{2}} d x

\frac{\partial}{\partial z} (5 e^{x} cos (yz))

What is the derivative of ((x+3)/(x-3))^5 ?
The derivative of ((x+3)/(x-3))^5 is -(30(x+3)^4)/((x-3)^6)
What is the first derivative of ((x+3)/(x-3))^5 ?
The first derivative of ((x+3)/(x-3))^5 is -(30(x+3)^4)/((x-3)^6)