What is (\partial)/(\partial x)(cos(-5x-6y)) ?

The answer to (\partial)/(\partial x)(cos(-5x-6y)) is -sin(5x+6y)*5

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(\partial)/(\partial x)(cos(-5x-6y))

\frac{\partial}{\partial x} (cos (- 5 x - 6 y))

- sin (5 x + 6 y) \cdot 5

Solution steps

\frac{\partial}{\partial x} (cos (- 5 x - 6 y))

Simplify

cos (- 5 x - 6 y) : cos (5 x + 6 y)

= \frac{\partial}{\partial x} (cos (5 x + 6 y))

Treat

y

as a constant

Apply the chain rule:

- sin (5 x + 6 y) \frac{\partial}{\partial x} (5 x + 6 y)

= - sin (5 x + 6 y) \frac{\partial}{\partial x} (5 x + 6 y)

\frac{\partial}{\partial x} (5 x + 6 y) = 5

= - sin (5 x + 6 y) \cdot 5

What is (\partial)/(\partial x)(cos(-5x-6y)) ?
The answer to (\partial)/(\partial x)(cos(-5x-6y)) is -sin(5x+6y)*5