What is (\partial)/(\partial y)(sin(x*y)) ?

The answer to (\partial)/(\partial y)(sin(x*y)) is cos(xy)x

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(\partial)/(\partial y)(sin(x*y))

\frac{\partial}{\partial y} (sin (x \cdot y))

cos (x y) x

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= cos (x y) x

(2 x^{2} - 3)^{3}

8 t^{2}

y^{^{'}} + 2 y = 60, y (1) = 80

\frac{d y}{d x} + \frac{3 y}{x} = x^{5} y^{3}

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

What is (\partial)/(\partial y)(sin(x*y)) ?
The answer to (\partial)/(\partial y)(sin(x*y)) is cos(xy)x