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Popular >

derivative of 1/2 x^3+3/(2x)

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Graph

Popular Examples

y^{''}-8y^'+16y=0,y(0)=1,y^'(0)=2

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = 1, y^{^{'}} (0) = 2

derivative of c^1e^{-x}+c^2e^{2x}

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

derivative of y= 5/(2x^3)derivative of

y = \frac{5}{2 x ^{3}}

(\partial}{\partial x}(e^{-(\frac{x^2+y^2)/2)})

\frac{\partial}{\partial x} (e^{- (\frac{x ^{2} + y ^{2}}{2})})

integral from 2 to 6 of x/(x^2+6x+13)

\int_{2}^{6} \frac{x}{x ^{2} + 6 x + 13} d x

Frequently Asked Questions (FAQ)

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