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

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

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

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

- π cos (π (x - y))

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= cos (π (x - y)) (- π)

Simplify

= - π cos (π (x - y))

y^{^{'}} = 5 y + y^{5}

\frac{d}{d x} (\frac{x ^{2}}{3 x + 7})

y = \frac{1}{f ( x )}

x^{\frac{1}{3}} - 1

\frac{d}{d t} (\frac{1}{( t + 1 ) ^{2}})

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