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Popular >

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

Solution

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

Solution

\frac{128 x ^{3}}{( x + 2 ) ^{5}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

4 (\frac{2 x}{x + 2})^{3} \frac{4}{( x + 2 ) ^{2}} : \frac{128 x ^{3}}{( x + 2 ) ^{5}}

= \frac{128 x ^{3}}{( x + 2 ) ^{5}}

Popular Examples

limit as x approaches 8 of ((x+6))/(x-8)

x \to 8 lim (\frac{( x + 6 )}{x - 8})

integral of (x^2)/((5+x^3)^2)

\int \frac{x ^{2}}{( 5 + x ^{3} ) ^{2}} d x

derivative of f(x)=-2cos(x)derivative of

f (x) = - 2 cos (x)

integral of sqrt(x)-2/(sqrt(x))

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

y^{''}+25y=sin(5t)

y^{^{''}} + 25 y = sin (5 t)

Frequently Asked Questions (FAQ)

What is the derivative of ((2x/(x+2))^4) ?
The derivative of ((2x/(x+2))^4) is (128x^3)/((x+2)^5)
What is the first derivative of ((2x/(x+2))^4) ?
The first derivative of ((2x/(x+2))^4) is (128x^3)/((x+2)^5)