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

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

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

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

cos (x y) y

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (x y) y

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