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

The derivative of x^{\sqrt[3]{x}} is x^{\sqrt[3]{x}}((ln(x))/(3x^{2/3)}+1/(x^{2/3)})

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

The first derivative of x^{\sqrt[3]{x}} is x^{\sqrt[3]{x}}((ln(x))/(3x^{2/3)}+1/(x^{2/3)})

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Solution steps

Apply exponent rule:

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

Apply the chain rule:

\int \frac{5 x - 2}{x ^{2} - 4} d x

\frac{d}{d x} (sin (8 x + 4))

\frac{d}{d x} ((f (x) (4 x))^{2} + 2)

\frac{d}{d x} (cos (a t))

\frac{9}{x ^{2}}

What is the derivative of x^{\sqrt[3]{x}} ?
The derivative of x^{\sqrt[3]{x}} is x^{\sqrt[3]{x}}((ln(x))/(3x^{2/3)}+1/(x^{2/3)})
What is the first derivative of x^{\sqrt[3]{x}} ?
The first derivative of x^{\sqrt[3]{x}} is x^{\sqrt[3]{x}}((ln(x))/(3x^{2/3)}+1/(x^{2/3)})