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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\frac{d}{d x} ((\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}}

\int \frac{x ^{3}}{x ^{2} - x - 2} d x

y = x + x^{π}

f (x) = \frac{1}{4 + 3 x}, at x = 2

y = - x^{- 1} + \frac{3}{5} x + \frac{1}{2}

\int (t^{2} + 2 t + 1)^{4} (t + 1) d t

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)