What is (\partial)/(\partial x)(sin(pi(2x-2y))) ?

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

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(\partial)/(\partial x)(sin(pi(2x-2y)))

\frac{\partial}{\partial x} (sin (π (2 x - 2 y)))

cos (π (2 x - 2 y)) \cdot 2 π

Solution steps

\frac{\partial}{\partial x} (sin (π (2 x - 2 y)))

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (π (2 x - 2 y)) \cdot 2 π

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