What is the derivative of (x^2)^x ?

The derivative of (x^2)^x is (x^2)^x(ln(x^2)+2)

What is the first derivative of (x^2)^x ?

The first derivative of (x^2)^x is (x^2)^x(ln(x^2)+2)

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derivative of

(x^{2})^{x}

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

Solution steps

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

Apply exponent rule:

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

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

= \frac{d}{d x} (e^{x l n (x^{2})})

Apply the chain rule:

e^{x l n (x^{2})} \frac{d}{d x} (x ln (x^{2}))

= e^{x l n (x^{2})} \frac{d}{d x} (x ln (x^{2}))

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

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

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

= (x^{2})^{x} (ln (x^{2}) + 2)

What is the derivative of (x^2)^x ?
The derivative of (x^2)^x is (x^2)^x(ln(x^2)+2)
What is the first derivative of (x^2)^x ?
The first derivative of (x^2)^x is (x^2)^x(ln(x^2)+2)