What is the derivative of ((x^2+2x/(x+1))^5) ?

The derivative of ((x^2+2x/(x+1))^5) is (5(x^2+2x)^4(x^2+2x+2))/((x+1)^6)

What is the first derivative of ((x^2+2x/(x+1))^5) ?

The first derivative of ((x^2+2x/(x+1))^5) is (5(x^2+2x)^4(x^2+2x+2))/((x+1)^6)

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\frac{d}{d x} ((\frac{x ^{2} + 2 x}{x + 1})^{5})

\frac{5 ( x ^{2} + 2 x ) ^{4} ( x ^{2} + 2 x + 2 )}{( x + 1 ) ^{6}}

Solution steps

\frac{d}{d x} ((\frac{x ^{2} + 2 x}{x + 1})^{5})

Apply the chain rule:

5 (\frac{x ^{2} + 2 x}{x + 1})^{4} \frac{d}{d x} (\frac{x ^{2} + 2 x}{x + 1})

= 5 (\frac{x ^{2} + 2 x}{x + 1})^{4} \frac{d}{d x} (\frac{x ^{2} + 2 x}{x + 1})

\frac{d}{d x} (\frac{x ^{2} + 2 x}{x + 1}) = \frac{x ^{2} + 2 x + 2}{( x + 1 ) ^{2}}

= 5 (\frac{x ^{2} + 2 x}{x + 1})^{4} \frac{x ^{2} + 2 x + 2}{( x + 1 ) ^{2}}

Simplify

5 (\frac{x ^{2} + 2 x}{x + 1})^{4} \frac{x ^{2} + 2 x + 2}{( x + 1 ) ^{2}} : \frac{5 ( x ^{2} + 2 x ) ^{4} ( x ^{2} + 2 x + 2 )}{( x + 1 ) ^{6}}

= \frac{5 ( x ^{2} + 2 x ) ^{4} ( x ^{2} + 2 x + 2 )}{( x + 1 ) ^{6}}

\frac{d}{d x} (9 ln (cos (x)))

\int sin^{3} (2 x) cos (2 x) d x

\frac{d}{d x} ((4 x^{2} - \frac{1}{2} x) (9 x + 8))

\frac{d}{d x} (3 e^{4 x})

2 y^{^{'}} = 3 x y + 1

What is the derivative of ((x^2+2x/(x+1))^5) ?
The derivative of ((x^2+2x/(x+1))^5) is (5(x^2+2x)^4(x^2+2x+2))/((x+1)^6)
What is the first derivative of ((x^2+2x/(x+1))^5) ?
The first derivative of ((x^2+2x/(x+1))^5) is (5(x^2+2x)^4(x^2+2x+2))/((x+1)^6)