What is (\partial)/(\partial y)(sin(pi(5x-2y))) ?

The answer to (\partial)/(\partial y)(sin(pi(5x-2y))) is -2picos(pi(5x-2y))

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(\partial)/(\partial y)(sin(pi(5x-2y)))

\frac{\partial}{\partial y} (sin (π (5 x - 2 y)))

- 2 π cos (π (5 x - 2 y))

Solution steps

\frac{\partial}{\partial y} (sin (π (5 x - 2 y)))

Treat

x

as a constant

Apply the chain rule:

cos (π (5 x - 2 y)) \frac{\partial}{\partial y} (π (5 x - 2 y))

= cos (π (5 x - 2 y)) \frac{\partial}{\partial y} (π (5 x - 2 y))

\frac{\partial}{\partial y} (π (5 x - 2 y)) = - 2 π

= cos (π (5 x - 2 y)) (- 2 π)

Simplify

= - 2 π cos (π (5 x - 2 y))

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\int \frac{2}{e ^{x} + e ^{- x}} d x

What is (\partial)/(\partial y)(sin(pi(5x-2y))) ?
The answer to (\partial)/(\partial y)(sin(pi(5x-2y))) is -2picos(pi(5x-2y))