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

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

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

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

cos (x - 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) = 1

= cos (x - y) \cdot 1

Simplify

= cos (x - y)

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