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Popular >

derivative of e^{x*ln(x})

Solution

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

Solution

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)

Popular Examples

derivative of 1/(xln^2(x))

\frac{d}{d x} (\frac{1}{x ln ^{2} ( x )})

tangent of y=tan(12x^2),\at x=sqrt(pi)tangent of

y = tan (12 x^{2}), at x = π

derivative of (x^2)^2 derivative of

(x^{2})^{2}

derivative of sec^2(0)derivative of

sec^{2} (0)

sum from n=1 to infinity of 2/(n^6)

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

Frequently Asked Questions (FAQ)

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