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{d}{d x} (x ln (5 x))

3 x^{2} - 4 x + 6, at x = 2

y^{^{''}} + 4 y = 0, y (0) = 1, y (1) = 0

\frac{d}{d t} (a e^{t} cos (2 t) + b e^{t} sin (2 t))

x \to 0 lim ((1 + x)^{2} - 1)

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)