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Popular Calculus >

derivative of (x^3-1/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Graph

Popular Examples

derivative of e^{-15x}

\frac{d}{d x} (e^{- 15 x})

(\partial)/(\partial x)(48x^3cos(6x^2y))

\frac{\partial}{\partial x} (48 x^{3} cos (6 x^{2} y))

derivative of (x-3/x)

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

integral of csc^2(u)

\int csc^{2} (u) d u

integral of sin(1/6 x)

\int sin (\frac{1}{6} x) d x

Frequently Asked Questions (FAQ)

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