What is the derivative of f(x)=((x-4)/(x+4))^4 ?

The derivative of f(x)=((x-4)/(x+4))^4 is (32(x-4)^3)/((x+4)^5)

What is the first derivative of f(x)=((x-4)/(x+4))^4 ?

The first derivative of f(x)=((x-4)/(x+4))^4 is (32(x-4)^3)/((x+4)^5)

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derivative of

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

\frac{32 ( x - 4 ) ^{3}}{( x + 4 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x - 4}{x + 4}) = \frac{8}{( x + 4 ) ^{2}}

= 4 (\frac{x - 4}{x + 4})^{3} \frac{8}{( x + 4 ) ^{2}}

Simplify

4 (\frac{x - 4}{x + 4})^{3} \frac{8}{( x + 4 ) ^{2}} : \frac{32 ( x - 4 ) ^{3}}{( x + 4 ) ^{5}}

= \frac{32 ( x - 4 ) ^{3}}{( x + 4 ) ^{5}}

What is the derivative of f(x)=((x-4)/(x+4))^4 ?
The derivative of f(x)=((x-4)/(x+4))^4 is (32(x-4)^3)/((x+4)^5)
What is the first derivative of f(x)=((x-4)/(x+4))^4 ?
The first derivative of f(x)=((x-4)/(x+4))^4 is (32(x-4)^3)/((x+4)^5)