What is (\partial)/(\partial x)(x^2y+4y) ?

The answer to (\partial)/(\partial x)(x^2y+4y) is 2xy

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(\partial)/(\partial x)(x^2y+4y)

\frac{\partial}{\partial x} (x^{2} y + 4 y)

2 x y

Solution steps

\frac{\partial}{\partial x} (x^{2} y + 4 y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (4 y)

\frac{\partial}{\partial x} (x^{2} y) = 2 y x

\frac{\partial}{\partial x} (4 y) = 0

= 2 y x + 0

Simplify

= 2 x y

\int \frac{- 5 x}{( x ^{2} + 5 ) ^{\frac{3}{2}}} d x

y = x ln (sin^{2} (x))

y (x + 7) + \frac{d y}{d x} = 0

\int \frac{- 1}{\frac{1}{4} - x ^{2}} d x

(e^{t} (5 - 3 e^{- 2 t}))^{^{'}}

What is (\partial)/(\partial x)(x^2y+4y) ?
The answer to (\partial)/(\partial x)(x^2y+4y) is 2xy