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Popular >

derivative of sqrt(x)*ln(x)

Solution

\frac{d}{d x} (x \cdot 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

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\frac{\partial}{\partial x} (x^{2 + y^{2}})

integral of (15x^4)

\int (15 x^{4}) d x

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\frac{d}{d x} (\frac{- 7 x ^{2}}{2 x ^{2} - 5})

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\frac{d}{d x} (- cos (5 x))

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\int 7 e^{4} d x

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))