What is (\partial)/(\partial y)(sin(3x-6y)) ?

The answer to (\partial)/(\partial y)(sin(3x-6y)) is -6cos(3x-6y)

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(\partial)/(\partial y)(sin(3x-6y))

\frac{\partial}{\partial y} (sin (3 x - 6 y))

- 6 cos (3 x - 6 y)

Solution steps

\frac{\partial}{\partial y} (sin (3 x - 6 y))

Treat

x

as a constant

Apply the chain rule:

cos (3 x - 6 y) \frac{\partial}{\partial y} (3 x - 6 y)

= cos (3 x - 6 y) \frac{\partial}{\partial y} (3 x - 6 y)

\frac{\partial}{\partial y} (3 x - 6 y) = - 6

= cos (3 x - 6 y) (- 6)

Simplify

= - 6 cos (3 x - 6 y)

What is (\partial)/(\partial y)(sin(3x-6y)) ?
The answer to (\partial)/(\partial y)(sin(3x-6y)) is -6cos(3x-6y)