What is the derivative of \sqrt[6]{x}^{ln(x)} ?

The derivative of \sqrt[6]{x}^{ln(x)} is (x^{ln(\sqrt[6]{x})-1}ln(x^2))/6

What is the first derivative of \sqrt[6]{x}^{ln(x)} ?

The first derivative of \sqrt[6]{x}^{ln(x)} is (x^{ln(\sqrt[6]{x})-1}ln(x^2))/6

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derivative of

6 x^{l n (x)}

\frac{x ^{l n (6 x) - 1} ln ( x ^{2} )}{6}

Solution steps

\frac{d}{d x} ((6 x)^{l n (x)})

Apply exponent rule:

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

(6 x)^{l n (x)} = e^{l n (x) l n (6 x)}

= \frac{d}{d x} (e^{l n (x) l n (6 x)})

Apply the chain rule:

e^{l n (x) l n (6 x)} \frac{d}{d x} (ln (x) ln (6 x))

= e^{l n (x) l n (6 x)} \frac{d}{d x} (ln (x) ln (6 x))

\frac{d}{d x} (ln (x) ln (6 x)) = \frac{ln ( x ^{2} )}{6 x}

= e^{l n (x) l n (6 x)} \frac{ln ( x ^{2} )}{6 x}

Simplify

e^{l n (x) l n (6 x)} \frac{ln ( x ^{2} )}{6 x} : \frac{x ^{l n (6 x) - 1} ln ( x ^{2} )}{6}

= \frac{x ^{l n (6 x) - 1} ln ( x ^{2} )}{6}

\int_{1}^{9} π (x - 1) d x

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

f (x) = \frac{5}{x}, (5, 1)

\frac{( x - 1 )}{x ^{2} + 3}

\int \frac{1}{( 9 - x ^{2} ) ^{\frac{3}{2}}} d x

What is the derivative of \sqrt[6]{x}^{ln(x)} ?
The derivative of \sqrt[6]{x}^{ln(x)} is (x^{ln(\sqrt[6]{x})-1}ln(x^2))/6
What is the first derivative of \sqrt[6]{x}^{ln(x)} ?
The first derivative of \sqrt[6]{x}^{ln(x)} is (x^{ln(\sqrt[6]{x})-1}ln(x^2))/6