What is the derivative of \sqrt[3]{x}^{ln(x}) ?

The derivative of \sqrt[3]{x}^{ln(x}) is (2e^{(ln^2(x))/3}ln(x))/(3x)

What is the first derivative of \sqrt[3]{x}^{ln(x}) ?

The first derivative of \sqrt[3]{x}^{ln(x}) is (2e^{(ln^2(x))/3}ln(x))/(3x)

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\frac{2 e ^{\frac{l n ^{2} ( x )}{3}} ln ( x )}{3 x}

Solution steps

Apply exponent rule:

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

Apply the chain rule:

Simplify

= \frac{2 e ^{\frac{l n ^{2} ( x )}{3}} ln ( x )}{3 x}

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What is the derivative of \sqrt[3]{x}^{ln(x}) ?
The derivative of \sqrt[3]{x}^{ln(x}) is (2e^{(ln^2(x))/3}ln(x))/(3x)
What is the first derivative of \sqrt[3]{x}^{ln(x}) ?
The first derivative of \sqrt[3]{x}^{ln(x}) is (2e^{(ln^2(x))/3}ln(x))/(3x)