What is (\partial)/(\partial x)(sin(y-5x)) ?

The answer to (\partial)/(\partial x)(sin(y-5x)) is -5cos(y-5x)

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(\partial)/(\partial x)(sin(y-5x))

\frac{\partial}{\partial x} (sin (y - 5 x))

- 5 cos (y - 5 x)

Solution steps

\frac{\partial}{\partial x} (sin (y - 5 x))

Treat

y

as a constant

Apply the chain rule:

cos (y - 5 x) \frac{\partial}{\partial x} (y - 5 x)

= cos (y - 5 x) \frac{\partial}{\partial x} (y - 5 x)

\frac{\partial}{\partial x} (y - 5 x) = - 5

= cos (y - 5 x) (- 5)

Simplify

= - 5 cos (y - 5 x)

What is (\partial)/(\partial x)(sin(y-5x)) ?
The answer to (\partial)/(\partial x)(sin(y-5x)) is -5cos(y-5x)