What is the derivative of (((x+11))/((x-11)))^5 ?

The derivative of (((x+11))/((x-11)))^5 is -(110(x+11)^4)/((x-11)^6)

What is the first derivative of (((x+11))/((x-11)))^5 ?

The first derivative of (((x+11))/((x-11)))^5 is -(110(x+11)^4)/((x-11)^6)

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derivative of

(\frac{( x + 11 )}{( x - 11 )})^{5}

- \frac{110 ( x + 11 ) ^{4}}{( x - 11 ) ^{6}}

Solution steps

\frac{d}{d x} ((\frac{x + 11}{x - 11})^{5})

Apply the chain rule:

5 (\frac{x + 11}{x - 11})^{4} \frac{d}{d x} (\frac{x + 11}{x - 11})

= 5 (\frac{x + 11}{x - 11})^{4} \frac{d}{d x} (\frac{x + 11}{x - 11})

\frac{d}{d x} (\frac{x + 11}{x - 11}) = - \frac{22}{( x - 11 ) ^{2}}

= 5 (\frac{x + 11}{x - 11})^{4} (- \frac{22}{( x - 11 ) ^{2}})

Simplify

5 (\frac{x + 11}{x - 11})^{4} (- \frac{22}{( x - 11 ) ^{2}}) : - \frac{110 ( x + 11 ) ^{4}}{( x - 11 ) ^{6}}

= - \frac{110 ( x + 11 ) ^{4}}{( x - 11 ) ^{6}}

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What is the derivative of (((x+11))/((x-11)))^5 ?
The derivative of (((x+11))/((x-11)))^5 is -(110(x+11)^4)/((x-11)^6)
What is the first derivative of (((x+11))/((x-11)))^5 ?
The first derivative of (((x+11))/((x-11)))^5 is -(110(x+11)^4)/((x-11)^6)