What is the derivative of f(x)=(\sqrt[7]{x})^{ln(x)} ?

The derivative of f(x)=(\sqrt[7]{x})^{ln(x)} is (x^{ln(\sqrt[7]{x})-1}ln(x^2))/7

What is the first derivative of f(x)=(\sqrt[7]{x})^{ln(x)} ?

The first derivative of f(x)=(\sqrt[7]{x})^{ln(x)} is (x^{ln(\sqrt[7]{x})-1}ln(x^2))/7

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derivative of

Solution steps

Apply exponent rule:

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

Apply the chain rule:

Simplify

e^{5 t}

\int (x^{3} + 2)^{\frac{1}{2}} \cdot x^{2} d x

\frac{d}{d x} (sec^{2} (5 x^{2}))

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

\int_{0}^{1} 2 π x (x^{5} - x^{6}) d x

What is the derivative of f(x)=(\sqrt[7]{x})^{ln(x)} ?
The derivative of f(x)=(\sqrt[7]{x})^{ln(x)} is (x^{ln(\sqrt[7]{x})-1}ln(x^2))/7
What is the first derivative of f(x)=(\sqrt[7]{x})^{ln(x)} ?
The first derivative of f(x)=(\sqrt[7]{x})^{ln(x)} is (x^{ln(\sqrt[7]{x})-1}ln(x^2))/7