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Popular >

derivative of y=e^xln(x)

Solution

derivative of

y = 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

(\partial)/(\partial x)(20-2x+1.5-y+3a)

\frac{\partial}{\partial x} (20 - 2 x + 1.5 - y + 3 a)

limit as x approaches-infinity of x*e^{1/x}

x \to - \infty lim (x \cdot e^{\frac{1}{x}})

integral of sqrt(4t^2+1)

\int 4 t^{2} + 1 d t

limit as x approaches 0 of-|x-2|+3

x \to 0 lim (- ∣ x - 2 ∣ + 3)

(\partial)/(\partial x)((x+y)/(x*y))

\frac{\partial}{\partial x} (\frac{x + y}{x \cdot y})

Frequently Asked Questions (FAQ)

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