What is the derivative of e^x*ln(x) ?

The derivative of e^x*ln(x) is e^xln(x)+(e^x)/x

What is the first derivative of e^x*ln(x) ?

The first derivative of e^x*ln(x) is e^xln(x)+(e^x)/x

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derivative of

e^{x} \cdot ln (x)

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}

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

\int 17 e^{- 17 x} d x

x \to 0 lim (x (1 + \frac{1}{x}))

y = \frac{( x - 1 )}{( x + 1 )}

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

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