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Popular >

derivative of (x^3+3/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Graph

Popular Examples

derivative of (x+1/(x^2+x-2))

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

integral of 7x^{2/5}+4x^{-4/5}

\int 7 x^{\frac{2}{5}} + 4 x^{- \frac{4}{5}} d x

integral of 6xsqrt(1+3^2)

\int 6 x 1 + 3^{2} d x

derivative of (((x+1)(x+2)))/(sqrt(x))derivative of

\frac{( ( x + 1 ) ( x + 2 ) )}{x}

limit as x approaches-3+of (-5x)/(x+3)

x \to - 3 + lim (\frac{- 5 x}{x + 3})

Frequently Asked Questions (FAQ)

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