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Popular >

derivative of (x^2/2+x*(ln(x)-1))

Solution

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

Solution

x + ln (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

= x + ln (x)

Popular Examples

limit as x approaches 3 of 4x^3-2x^2+x-6

x \to 3 lim (4 x^{3} - 2 x^{2} + x - 6)

tangent of y= 8/(1-t),(-1,4)tangent of

y = \frac{8}{1 - t}, (- 1, 4)

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

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

tangent of y=9x-2x^2,(-2,-26)tangent of

y = 9 x - 2 x^{2}, (- 2, - 26)

derivative of (6x/(6+sqrt(x)))

\frac{d}{d x} (\frac{6 x}{6 + x})

Frequently Asked Questions (FAQ)

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