What is the derivative of \sqrt[3]{x}*tan(5x) ?

The derivative of \sqrt[3]{x}*tan(5x) is (tan(5x))/(3x^{2/3)}+5\sqrt[3]{x}sec^2(5x)

What is the first derivative of \sqrt[3]{x}*tan(5x) ?

The first derivative of \sqrt[3]{x}*tan(5x) is (tan(5x))/(3x^{2/3)}+5\sqrt[3]{x}sec^2(5x)

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Solution steps

Apply the Product Rule:

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

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

\frac{1}{3 x ^{\frac{2}{3}}} tan (5 x) = \frac{tan ( 5 x )}{3 x ^{\frac{2}{3}}}

\frac{d}{d x} (sec (x^{3}))

\int x \cdot e^{- a \cdot x} d x

\int_{1}^{4} π (x - 1)^{2} d x

\frac{d y}{d x} = - \frac{6 x}{y}

\frac{200}{t + 2}

What is the derivative of \sqrt[3]{x}*tan(5x) ?
The derivative of \sqrt[3]{x}*tan(5x) is (tan(5x))/(3x^{2/3)}+5\sqrt[3]{x}sec^2(5x)
What is the first derivative of \sqrt[3]{x}*tan(5x) ?
The first derivative of \sqrt[3]{x}*tan(5x) is (tan(5x))/(3x^{2/3)}+5\sqrt[3]{x}sec^2(5x)