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Popular >

derivative of ((2x/(x+1))^4)

Solution

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

Solution

\frac{64 x ^{3}}{( x + 1 ) ^{5}}

Solution steps

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

Apply the chain rule:

4 (\frac{2 x}{x + 1})^{3} \frac{d}{d x} (\frac{2 x}{x + 1})

= 4 (\frac{2 x}{x + 1})^{3} \frac{d}{d x} (\frac{2 x}{x + 1})

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

= 4 (\frac{2 x}{x + 1})^{3} \frac{2}{( x + 1 ) ^{2}}

Simplify

4 (\frac{2 x}{x + 1})^{3} \frac{2}{( x + 1 ) ^{2}} : \frac{64 x ^{3}}{( x + 1 ) ^{5}}

= \frac{64 x ^{3}}{( x + 1 ) ^{5}}

Graph

Popular Examples

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

\frac{d}{d y} (e^{3 y})

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

limit as x approaches 0 of 5x+3-2x^2

x \to 0 lim (5 x + 3 - 2 x^{2})

area x=7y^2,x=4+6y^2 area

x = 7 y^{2}, x = 4 + 6 y^{2}

Frequently Asked Questions (FAQ)

What is the derivative of ((2x/(x+1))^4) ?
The derivative of ((2x/(x+1))^4) is (64x^3)/((x+1)^5)
What is the first derivative of ((2x/(x+1))^4) ?
The first derivative of ((2x/(x+1))^4) is (64x^3)/((x+1)^5)