What is the derivative of e^{xln(x}) ?

The derivative of e^{xln(x}) is x^x(ln(x)+1)

What is the first derivative of e^{xln(x}) ?

The first derivative of e^{xln(x}) is x^x(ln(x)+1)

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\frac{d}{d x} (e^{x l n (x)})

x^{x} (ln (x) + 1)

Solution steps

\frac{d}{d x} (e^{x l n (x)})

Simplify

e^{x l n (x)} : x^{x}

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

x^{x} = e^{x l n (x)}

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

Apply the chain rule:

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

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

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

= e^{x l n (x)} (ln (x) + 1)

e^{x l n (x)} = x^{x}

= x^{x} (ln (x) + 1)

x \to 0 lim ((e^{x} + x)^{\frac{m}{x}})

\int \frac{7}{9 - 49 x ^{2}} d x

{\frac{1}{s ^{4}}}

2, - 5, y = 2 x^{2} + 12, y = 0

x \to \infty lim (4 + \frac{1}{x})

What is the derivative of e^{xln(x}) ?
The derivative of e^{xln(x}) is x^x(ln(x)+1)
What is the first derivative of e^{xln(x}) ?
The first derivative of e^{xln(x}) is x^x(ln(x)+1)