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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

y^{''}+6y^'+25y=0,y(0)=2,y^'(0)=-5

y^{^{''}} + 6 y^{^{'}} + 25 y = 0, y (0) = 2, y^{^{'}} (0) = - 5

integral from 0 to 7 of k(7-x)

\int_{0}^{7} k (7 - x)

limit as t approaches+0 of 18(1.15)^t

t \to + 0 lim (18 (1.15)^{t})

limit as x approaches 7+of (9x)/(x-7)

x \to 7 + lim (\frac{9 x}{x - 7})

integral of 2x+3e^x

\int 2 x + 3 e^{x} d x

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