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Popular >

derivative of e^xln(x)

Solution

derivative of

e^{x} ln (x)

Solution

e^{x} ln (x) + \frac{e ^{x}}{x}

Solution steps

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

Apply the Product Rule:

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

f = e^{x}, g = ln (x)

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

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

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

= e^{x} ln (x) + \frac{1}{x} e^{x}

\frac{1}{x} e^{x} = \frac{e ^{x}}{x}

= e^{x} ln (x) + \frac{e ^{x}}{x}

Popular Examples

sum from n=1 to infinity of 1/(n^2+7n)

n = 1 \sum \infty \frac{1}{n ^{2} + 7 n}

derivative of F(x)=(x^4+9x^2-7)^8 derivative of

F (x) = (x^{4} + 9 x^{2} - 7)^{8}

integral from 3 to 9 of 8/x

\int_{3}^{9} \frac{8}{x} d x

limit as x approaches 4 of (7+x)/(4-x)

x \to 4 lim (\frac{7 + x}{4 - x})

limit as x approaches 0 of x/(sin^2(0))

x \to 0 lim (\frac{x}{sin ^{2} ( 0 )})

Frequently Asked Questions (FAQ)

What is the derivative of e^xln(x) ?
The derivative of e^xln(x) is e^xln(x)+(e^x)/x
What is the first derivative of e^xln(x) ?
The first derivative of e^xln(x) is e^xln(x)+(e^x)/x