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

The derivative of ((x-5)/(x+5))^4 is (40(x-5)^3)/((x+5)^5)

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

The first derivative of ((x-5)/(x+5))^4 is (40(x-5)^3)/((x+5)^5)

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derivative of

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

\frac{40 ( x - 5 ) ^{3}}{( x + 5 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (\frac{x - 5}{x + 5}) = \frac{10}{( x + 5 ) ^{2}}

= 4 (\frac{x - 5}{x + 5})^{3} \frac{10}{( x + 5 ) ^{2}}

Simplify

4 (\frac{x - 5}{x + 5})^{3} \frac{10}{( x + 5 ) ^{2}} : \frac{40 ( x - 5 ) ^{3}}{( x + 5 ) ^{5}}

= \frac{40 ( x - 5 ) ^{3}}{( x + 5 ) ^{5}}

10 y^{^{''}} + 1000 y = 50 cos (8 t)

\frac{d}{d x} (e^{- x} (1 - x))

3 π r^{2}

\frac{d}{d x} (x^{2} e^{- 0.04 x})

\frac{\partial}{\partial y} (x e^{- 2 x})

What is the derivative of ((x-5)/(x+5))^4 ?
The derivative of ((x-5)/(x+5))^4 is (40(x-5)^3)/((x+5)^5)
What is the first derivative of ((x-5)/(x+5))^4 ?
The first derivative of ((x-5)/(x+5))^4 is (40(x-5)^3)/((x+5)^5)