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

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

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

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

2 x y

Solution steps

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

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

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

= 2 y x + 0

Simplify

= 2 x y

f (x) = - 3 x^{3} + 2 x^{2} - 4 x + 7

\frac{d}{d x} (2.873 sec (x))

\int (\frac{1}{1 + sin ( x )}) d x

y = (x^{2} - x) ln (6 x), at x = 2

\int x x + 2 d x

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