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Popular >

derivative of xsqrt(ln(x))

Solution

derivative of

x ln (x)

Solution

ln (x) + \frac{1}{2 ln ( x )}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot ln (x) + \frac{1}{2 x ln ( x )} x

Simplify

1 \cdot ln (x) + \frac{1}{2 x ln ( x )} x : ln (x) + \frac{1}{2 ln ( x )}

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

Popular Examples

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

\int \frac{e ^{- x}}{e ^{- x} + 1} d x

derivative of 6e^{-2x}cos(4x)derivative of

6 e^{- 2 x} cos (4 x)

derivative of f(x)=5x^2-2x-7 derivative of

f (x) = 5 x^{2} - 2 x - 7

y^'=0.04y-2000,y(0)=25000

y^{^{'}} = 0.04 y - 2000, y (0) = 25000

laplacetransform e^{3(t-2)}laplace transform

e^{3 (t - 2)}

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(ln(x)) ?
The derivative of xsqrt(ln(x)) is sqrt(ln(x))+1/(2sqrt(ln(x)))
What is the first derivative of xsqrt(ln(x)) ?
The first derivative of xsqrt(ln(x)) is sqrt(ln(x))+1/(2sqrt(ln(x)))