What is the derivative of f(x)=((x+11)/(x-11))^6 ?

The derivative of f(x)=((x+11)/(x-11))^6 is -(132(x+11)^5)/((x-11)^7)

What is the first derivative of f(x)=((x+11)/(x-11))^6 ?

The first derivative of f(x)=((x+11)/(x-11))^6 is -(132(x+11)^5)/((x-11)^7)

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derivative of

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

- \frac{132 ( x + 11 ) ^{5}}{( x - 11 ) ^{7}}

Solution steps

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

Apply the chain rule:

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

= 6 (\frac{x + 11}{x - 11})^{5} \frac{d}{d x} (\frac{x + 11}{x - 11})

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

= 6 (\frac{x + 11}{x - 11})^{5} (- \frac{22}{( x - 11 ) ^{2}})

Simplify

6 (\frac{x + 11}{x - 11})^{5} (- \frac{22}{( x - 11 ) ^{2}}) : - \frac{132 ( x + 11 ) ^{5}}{( x - 11 ) ^{7}}

= - \frac{132 ( x + 11 ) ^{5}}{( x - 11 ) ^{7}}

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What is the derivative of f(x)=((x+11)/(x-11))^6 ?
The derivative of f(x)=((x+11)/(x-11))^6 is -(132(x+11)^5)/((x-11)^7)
What is the first derivative of f(x)=((x+11)/(x-11))^6 ?
The first derivative of f(x)=((x+11)/(x-11))^6 is -(132(x+11)^5)/((x-11)^7)