What is the derivative of ((x+6)/(x-6))^5 ?

The derivative of ((x+6)/(x-6))^5 is -(60(x+6)^4)/((x-6)^6)

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

The first derivative of ((x+6)/(x-6))^5 is -(60(x+6)^4)/((x-6)^6)

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derivative of

(\frac{x + 6}{x - 6})^{5}

- \frac{60 ( x + 6 ) ^{4}}{( x - 6 ) ^{6}}

Solution steps

\frac{d}{d x} ((\frac{x + 6}{x - 6})^{5})

Apply the chain rule:

5 (\frac{x + 6}{x - 6})^{4} \frac{d}{d x} (\frac{x + 6}{x - 6})

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

\frac{d}{d x} (\frac{x + 6}{x - 6}) = - \frac{12}{( x - 6 ) ^{2}}

= 5 (\frac{x + 6}{x - 6})^{4} (- \frac{12}{( x - 6 ) ^{2}})

Simplify

5 (\frac{x + 6}{x - 6})^{4} (- \frac{12}{( x - 6 ) ^{2}}) : - \frac{60 ( x + 6 ) ^{4}}{( x - 6 ) ^{6}}

= - \frac{60 ( x + 6 ) ^{4}}{( x - 6 ) ^{6}}

\frac{d}{d x} (e^{- \frac{x}{3}})

\int (1 - x^{2})^{2} x^{2} d x

\int 7 z^{3} e^{z} d z

y = 3 x^{4} - 3 x^{2}, y = 8 x^{2}

y = (2 x - 3)^{4} (x^{2} + x + 1)^{5}

What is the derivative of ((x+6)/(x-6))^5 ?
The derivative of ((x+6)/(x-6))^5 is -(60(x+6)^4)/((x-6)^6)
What is the first derivative of ((x+6)/(x-6))^5 ?
The first derivative of ((x+6)/(x-6))^5 is -(60(x+6)^4)/((x-6)^6)