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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

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

\frac{\partial}{\partial x} (\frac{x}{x + y ^{2}})

y^{^{'''}} - 2 y^{^{''}} - y^{^{'}} + 2 y = 0

3 r = \frac{d r}{d θ} - θ^{3}

\int cos (\frac{1}{5} x) d x

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