What is the derivative of x^4(1-2/(x+1)) ?

The derivative of x^4(1-2/(x+1)) is (4x^5+2x^4-4x^3)/((x+1)^2)

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

The first derivative of x^4(1-2/(x+1)) is (4x^5+2x^4-4x^3)/((x+1)^2)

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{4}, g = 1 - \frac{2}{x + 1}

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

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

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

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

Simplify

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

= \frac{4 x ^{5} + 2 x ^{4} - 4 x ^{3}}{( x + 1 ) ^{2}}

\frac{d}{d x} ((x - 1) sin (\frac{1}{x - 1}))

\frac{\partial}{\partial z} (3 x^{\frac{y}{z}})

e^{x} \frac{( 2 x + 5 ) ^{2}}{x - 2}

y^{^{'}} = - 2 y + x

3 sin^{3} (x)

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