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Popular >

derivative of y=(x^3)/6+1/(2x)

Solution

derivative of

y = \frac{x ^{3}}{6} + \frac{1}{2 x}

Solution

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

Solution steps

\frac{d}{d x} (\frac{x ^{3}}{6} + \frac{1}{2 x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{3}}{6}) + \frac{d}{d x} (\frac{1}{2 x})

\frac{d}{d x} (\frac{x ^{3}}{6}) = \frac{x ^{2}}{2}

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

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

Popular Examples

derivative of x-cos(x)derivative of

x - cos (x)

integral from 0 to 2 of 6t

\int_{0}^{2} 6 t d t

(\partial)/(\partial x)(1/(x-3))

\frac{\partial}{\partial x} (\frac{1}{x - 3})

(\partial)/(\partial x)(sqrt((2x-3y)^3))

\frac{\partial}{\partial x} ((2 x - 3 y)^{3})

sum from n=1 to infinity}(x^{2n of)/(n!)

n = 1 \sum \infty \frac{x ^{2 n}}{n !}

Frequently Asked Questions (FAQ)

What is the derivative of y=(x^3)/6+1/(2x) ?
The derivative of y=(x^3)/6+1/(2x) is (x^2)/2-1/(2x^2)
What is the first derivative of y=(x^3)/6+1/(2x) ?
The first derivative of y=(x^3)/6+1/(2x) is (x^2)/2-1/(2x^2)