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Popular >

derivative of sqrt(x)ln(x)

Solution

derivative of

x ln (x)

Solution

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches+2 of ((x^2-2x))/((x^2-4x+4))

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

derivative of x^2y derivative of

x^{2} y

d/(dt)(2sin(2t))

\frac{d}{d t} (2 sin (2 t))

derivative of (3x+1)/(x^2+1)derivative of

\frac{3 x + 1}{x ^{2} + 1}

y^{^{'}} = x + y, y (0) = 1

Frequently Asked Questions (FAQ)

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