What is (\partial)/(\partial x)(cos^2(x-y)) ?

The answer to (\partial)/(\partial x)(cos^2(x-y)) is -sin(2(x-y))

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(\partial)/(\partial x)(cos^2(x-y))

\frac{\partial}{\partial x} (cos^{2} (x - y))

- sin (2 (x - y))

Solution steps

\frac{\partial}{\partial x} (cos^{2} (x - y))

Treat

y

as a constant

Apply the chain rule:

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

= 2 cos (x - y) \frac{\partial}{\partial x} (cos (x - y))

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

= 2 cos (x - y) (- sin (x - y))

Simplify

2 cos (x - y) (- sin (x - y)) : - sin (2 (x - y))

= - sin (2 (x - y))

What is (\partial)/(\partial x)(cos^2(x-y)) ?
The answer to (\partial)/(\partial x)(cos^2(x-y)) is -sin(2(x-y))