What is (\partial)/(\partial x)(sin(7y-x)) ?

The answer to (\partial)/(\partial x)(sin(7y-x)) is -cos(7y-x)

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(\partial)/(\partial x)(sin(7y-x))

\frac{\partial}{\partial x} (sin (7 y - x))

- cos (7 y - x)

Solution steps

\frac{\partial}{\partial x} (sin (7 y - x))

Treat

y

as a constant

Apply the chain rule:

cos (7 y - x) \frac{\partial}{\partial x} (7 y - x)

= cos (7 y - x) \frac{\partial}{\partial x} (7 y - x)

\frac{\partial}{\partial x} (7 y - x) = - 1

= cos (7 y - x) (- 1)

Simplify

= - cos (7 y - x)

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What is (\partial)/(\partial x)(sin(7y-x)) ?
The answer to (\partial)/(\partial x)(sin(7y-x)) is -cos(7y-x)