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

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

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(\partial)/(\partial y)(x^2+sin(xy))

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

x cos (x y)

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (x^{2}) = 0

\frac{\partial}{\partial y} (sin (x y)) = cos (x y) x

= 0 + cos (x y) x

Simplify

= x cos (x y)

\int_{0}^{1} cos (x) d x

4 y^{^{''}} - y^{^{'}} + 2 y = 0, y (0) = 2, y^{^{'}} (0) = 0

x \to 3 lim (\frac{3 - x}{∣ 3 - x ∣})

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

x \to - \infty lim (0^{x})

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