What is (\partial)/(\partial y)(5xy^3) ?

The answer to (\partial)/(\partial y)(5xy^3) is 15xy^2

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(\partial)/(\partial y)(5xy^3)

\frac{\partial}{\partial y} (5 x y^{3})

15 x y^{2}

Solution steps

\frac{\partial}{\partial y} (5 x y^{3})

Treat

x

as a constant

Take the constant out:

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

= 5 x \frac{\partial}{\partial y} (y^{3})

Apply the Power Rule:

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

= 5 x \cdot 3 y^{3 - 1}

Simplify

= 15 x y^{2}

y = x^{2} + 5 x + 2, (- 5, 2)

f (x) = - 3 - 6 x^{2}, (- 2, 27)

f (t) = t sin (t)

\frac{d}{d x} (tan (\frac{x ^{2}}{2 x + 3}))

\int - csc (x) d x

What is (\partial)/(\partial y)(5xy^3) ?
The answer to (\partial)/(\partial y)(5xy^3) is 15xy^2