What is the derivative of \sqrt[4]{x}^{ln(x}) ?

The derivative of \sqrt[4]{x}^{ln(x}) is (e^{(ln^2(x))/4}ln(x))/(2x)

What is the first derivative of \sqrt[4]{x}^{ln(x}) ?

The first derivative of \sqrt[4]{x}^{ln(x}) is (e^{(ln^2(x))/4}ln(x))/(2x)

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\frac{e ^{\frac{l n ^{2} ( x )}{4}} ln ( x )}{2 x}

Solution steps

Apply exponent rule:

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

Apply the chain rule:

Simplify

= \frac{e ^{\frac{l n ^{2} ( x )}{4}} ln ( x )}{2 x}

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x \to - \infty lim (\frac{7 x ^{4} - 14 x ^{2}}{6 x ^{5} + 3})

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What is the derivative of \sqrt[4]{x}^{ln(x}) ?
The derivative of \sqrt[4]{x}^{ln(x}) is (e^{(ln^2(x))/4}ln(x))/(2x)
What is the first derivative of \sqrt[4]{x}^{ln(x}) ?
The first derivative of \sqrt[4]{x}^{ln(x}) is (e^{(ln^2(x))/4}ln(x))/(2x)