What is (\partial)/(\partial y)(x^2y+e^{xy}) ?

The answer to (\partial)/(\partial y)(x^2y+e^{xy}) is x^2+e^{xy}x

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(\partial)/(\partial y)(x^2y+e^{xy})

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

x^{2} + e^{x y} x

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= x^{2} + e^{x y} x

\frac{d}{d x} (x + 6)

\int 3 cos^{5} (x) sin^{4} (x) d x

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

x \to \infty lim (\frac{1}{x} + 2)

y^{^{''}} + (a + b) y = 0

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