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

The derivative of f(x)=((x+4)/(x-4))^5 is -(40(x+4)^4)/((x-4)^6)

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

The first derivative of f(x)=((x+4)/(x-4))^5 is -(40(x+4)^4)/((x-4)^6)

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derivative of

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

- \frac{40 ( x + 4 ) ^{4}}{( x - 4 ) ^{6}}

Solution steps

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

Apply the chain rule:

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

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

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

= 5 (\frac{x + 4}{x - 4})^{4} (- \frac{8}{( x - 4 ) ^{2}})

Simplify

5 (\frac{x + 4}{x - 4})^{4} (- \frac{8}{( x - 4 ) ^{2}}) : - \frac{40 ( x + 4 ) ^{4}}{( x - 4 ) ^{6}}

= - \frac{40 ( x + 4 ) ^{4}}{( x - 4 ) ^{6}}

(1 - x^{2}) y^{^{'}} + x y = a x

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

\int_{0}^{9} 2 π y (\frac{y}{3}) d y

e^{\frac{x}{x - 4}}

\frac{8 s + 2}{s ^{2} - 25}

What is the derivative of f(x)=((x+4)/(x-4))^5 ?
The derivative of f(x)=((x+4)/(x-4))^5 is -(40(x+4)^4)/((x-4)^6)
What is the first derivative of f(x)=((x+4)/(x-4))^5 ?
The first derivative of f(x)=((x+4)/(x-4))^5 is -(40(x+4)^4)/((x-4)^6)