What is the derivative of f(x)=((x+7)/(x+9))^6 ?

The derivative of f(x)=((x+7)/(x+9))^6 is (12(x+7)^5)/((x+9)^7)

What is the first derivative of f(x)=((x+7)/(x+9))^6 ?

The first derivative of f(x)=((x+7)/(x+9))^6 is (12(x+7)^5)/((x+9)^7)

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derivative of

f (x) = (\frac{x + 7}{x + 9})^{6}

\frac{12 ( x + 7 ) ^{5}}{( x + 9 ) ^{7}}

Solution steps

\frac{d}{d x} ((\frac{x + 7}{x + 9})^{6})

Apply the chain rule:

6 (\frac{x + 7}{x + 9})^{5} \frac{d}{d x} (\frac{x + 7}{x + 9})

= 6 (\frac{x + 7}{x + 9})^{5} \frac{d}{d x} (\frac{x + 7}{x + 9})

\frac{d}{d x} (\frac{x + 7}{x + 9}) = \frac{2}{( x + 9 ) ^{2}}

= 6 (\frac{x + 7}{x + 9})^{5} \frac{2}{( x + 9 ) ^{2}}

Simplify

6 (\frac{x + 7}{x + 9})^{5} \frac{2}{( x + 9 ) ^{2}} : \frac{12 ( x + 7 ) ^{5}}{( x + 9 ) ^{7}}

= \frac{12 ( x + 7 ) ^{5}}{( x + 9 ) ^{7}}

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What is the derivative of f(x)=((x+7)/(x+9))^6 ?
The derivative of f(x)=((x+7)/(x+9))^6 is (12(x+7)^5)/((x+9)^7)
What is the first derivative of f(x)=((x+7)/(x+9))^6 ?
The first derivative of f(x)=((x+7)/(x+9))^6 is (12(x+7)^5)/((x+9)^7)