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

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

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

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

2 x y

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

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

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

= 2 y x + 0

Simplify

= 2 x y

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

y^{^{'''}} - 6 y^{^{''}} - y^{^{'}} + 6 y = 0

y^{^{''}} + 10 y^{^{'}} + 25 y = 3 e^{- 5 t}

\int_{- 6}^{6} 36 - x^{2} d x

\int \frac{1 + t}{t} d t

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