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

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

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

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

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

- \frac{x ^{3} + 1}{x ^{2}}

Solution steps

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

Simplify

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

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

f (x) = \frac{40 x ^{5}}{e ^{x}}

\int \frac{e ^{x}}{5 + e ^{x}} d x

n = 1 \sum \infty \frac{n ^{5}}{4 ^{n}}

\int_{2}^{\infty} 0 d x

\int - F x - x d x

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