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

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

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

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

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

- \frac{x ^{2} - 2}{x ^{2}}

Solution steps

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

Simplify

\frac{x ^{3} + x - 2}{x - x ^{2}} : - \frac{x ^{2} + x + 2}{x}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

= - \frac{x ^{2} - 2}{x ^{2}}

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

e^{3 e^{x}}

f (x) = 2 x^{2}, at x = - 1

\int_{2}^{6} (\frac{1}{x - 2}) d x

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