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

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

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

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

15 x^{2} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

= 15 x^{2} y

(- 41.38, 4.9), (2.38, 3.7)

\frac{d}{d x} (x + \frac{1}{4} sin^{2} (2 x))

f (t) = 1 - 6 t

e^{40 x}

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{- t} + e^{- t} cos (2 t)

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