What is (\partial)/(\partial y)(xy^3) ?

The answer to (\partial)/(\partial y)(xy^3) is 3xy^2

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(\partial)/(\partial y)(xy^3)

\frac{\partial}{\partial y} (x y^{3})

3 x y^{2}

Solution steps

\frac{\partial}{\partial y} (x y^{3})

Treat

x

as a constant

Take the constant out:

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

= x \frac{\partial}{\partial y} (y^{3})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= x \cdot 3 y^{3 - 1}

Simplify

= 3 x y^{2}

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

\int \frac{( 2 x ^{2} + 9 x + 2 )}{( x ^{2} + 1 ) ^{2}} d x

\int \frac{2 x + 1}{x ^{2} - 1} d x

\int \frac{7}{3} d x

\frac{1}{x}, at x = 4

What is (\partial)/(\partial y)(xy^3) ?
The answer to (\partial)/(\partial y)(xy^3) is 3xy^2