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

The derivative of x^{xln(x}) is e^{xln^2(x)}(ln^2(x)+2ln(x))

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

The first derivative of x^{xln(x}) is e^{xln^2(x)}(ln^2(x)+2ln(x))

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

e^{x l n^{2} (x)} (ln^{2} (x) + 2 ln (x))

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (x ln (x) ln (x)) = ln^{2} (x) + 2 ln (x)

= e^{x l n (x) l n (x)} (ln^{2} (x) + 2 ln (x))

Simplify

x ln (x) ln (x) : x ln^{2} (x)

= e^{x l n^{2} (x)} (ln^{2} (x) + 2 ln (x))

\int e^{- p x} d x

(7 x^{6} + 8 x^{3})^{4}

\int \frac{y ^{2} - x ^{2}}{( x ^{2} + y ^{2} ) ^{2}} d y

n = 2 \sum \infty \frac{6}{( n ^{2} - 1 )}

\frac{d}{d x} (\frac{9 - x ^{2}}{4 x})

What is the derivative of x^{xln(x}) ?
The derivative of x^{xln(x}) is e^{xln^2(x)}(ln^2(x)+2ln(x))
What is the first derivative of x^{xln(x}) ?
The first derivative of x^{xln(x}) is e^{xln^2(x)}(ln^2(x)+2ln(x))