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Popular Calculus >

derivative of (x^2/8-1/x)

Solution

\frac{d}{d x} (\frac{x ^{2}}{8} - \frac{1}{x})

Solution

\frac{x}{4} + \frac{1}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{8} - \frac{1}{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{2}}{8}) - \frac{d}{d x} (\frac{1}{x})

\frac{d}{d x} (\frac{x ^{2}}{8}) = \frac{x}{4}

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

= \frac{x}{4} - (- \frac{1}{x ^{2}})

Simplify

= \frac{x}{4} + \frac{1}{x ^{2}}

Graph

Popular Examples

integral of 1/(3x^2+4)

\int \frac{1}{3 x ^{2} + 4} d x

tangent of y=3x+6cos(x),(pi/3 ,pi+3)

t an g e n t y = 3 x + 6 cos (x), (\frac{π}{3}, π + 3)

derivative of y=(x^2+8)^2-4x

d er i v a t i v e y = (x^{2} + 8)^{2} - 4 x

derivative of (x^5/(10))

\frac{d}{d x} (\frac{x ^{5}}{10})

limit as x approaches infinity of 4x+2

x \to \infty lim (4 x + 2)

Frequently Asked Questions (FAQ)

What is the derivative of (x^2/8-1/x) ?
The derivative of (x^2/8-1/x) is x/4+1/(x^2)
What is the first derivative of (x^2/8-1/x) ?
The first derivative of (x^2/8-1/x) is x/4+1/(x^2)