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Popular >

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

Solution

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

Solution

\frac{x}{4} - \frac{1}{x}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= \frac{x}{4} - \frac{1}{x}

Popular Examples

integral of (e^x)/((e^x-3)(e^{2x)+1)}

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

derivative of e^{x^2-y}

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

integral of 2x(x^2+5)^{-4}

\int 2 x (x^{2} + 5)^{- 4} d x

area x^2+6,12+4x-x^2 area

x^{2} + 6, 12 + 4 x - x^{2}

sum from n=1 to infinity of 0.4^n

n = 1 \sum \infty 0. 4^{n}

Frequently Asked Questions (FAQ)

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