What is the derivative of xy^{1/3} ?

The derivative of xy^{1/3} is y^{1/3}

What is the first derivative of xy^{1/3} ?

The first derivative of xy^{1/3} is y^{1/3}

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derivative of

x y^{\frac{1}{3}}

y^{\frac{1}{3}}

Solution steps

\frac{d}{d x} (x y^{\frac{1}{3}})

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= y^{\frac{1}{3}} \frac{d x}{d x}

Apply the common derivative:

\frac{d x}{d x} = 1

= y^{\frac{1}{3}} \cdot 1

Simplify

= y^{\frac{1}{3}}

What is the derivative of xy^{1/3} ?
The derivative of xy^{1/3} is y^{1/3}
What is the first derivative of xy^{1/3} ?
The first derivative of xy^{1/3} is y^{1/3}