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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{2 x}{x ^{2} + 1}

x^{3}, at x = 0

(0, - 5), (- 3, 5)

x \to 0 - lim (e^{\frac{4}{x}})

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

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