What is the derivative of (x^{10})^x ?

The derivative of (x^{10})^x is (x^{10})^x(ln(x^{10})+10)

What is the first derivative of (x^{10})^x ?

The first derivative of (x^{10})^x is (x^{10})^x(ln(x^{10})+10)

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derivative of

(x^{10})^{x}

(x^{10})^{x} (ln (x^{10}) + 10)

Solution steps

\frac{d}{d x} ((x^{10})^{x})

Apply exponent rule:

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

(x^{10})^{x} = e^{x l n (x^{10})}

= \frac{d}{d x} (e^{x l n (x^{10})})

Apply the chain rule:

e^{x l n (x^{10})} \frac{d}{d x} (x ln (x^{10}))

= e^{x l n (x^{10})} \frac{d}{d x} (x ln (x^{10}))

\frac{d}{d x} (x ln (x^{10})) = ln (x^{10}) + 10

= e^{x l n (x^{10})} (ln (x^{10}) + 10)

e^{x l n (x^{10})} = (x^{10})^{x}

= (x^{10})^{x} (ln (x^{10}) + 10)

\frac{8 x ^{2}}{3}

(1 - tan^{2} (x)) 3 (1 - sec^{2} (x)) 4

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

x^{3} - 2 x^{2} - 3

y = cos (lo g_{4} (x))

What is the derivative of (x^{10})^x ?
The derivative of (x^{10})^x is (x^{10})^x(ln(x^{10})+10)
What is the first derivative of (x^{10})^x ?
The first derivative of (x^{10})^x is (x^{10})^x(ln(x^{10})+10)