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

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

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

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

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Solution steps

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{1}{3 x ^{\frac{2}{3}}} e^{x} = \frac{e ^{x}}{3 x ^{\frac{2}{3}}}

\frac{d}{d t} (1 - t^{2})

\frac{\partial}{\partial x} (\frac{4}{x y})

\frac{d y}{d t} = e^{2 (t)} - 3 y, y (0) = 1

\int_{- 1}^{0} 3 u + 4 d u

\int x^{9} x^{5} + 5 d x

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