What is (\partial)/(\partial x)(sin(pixy)) ?

The answer to (\partial)/(\partial x)(sin(pixy)) is cos(pixy)piy

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(\partial)/(\partial x)(sin(pixy))

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

cos (π x y) π y

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= cos (π x y) π y

2 x - 1, \frac{1}{x}, x = 3

\frac{d y}{d x} = \frac{1}{( 2 x + y + 1 )}

\frac{d y}{d t} = \frac{y}{t}

y = \frac{x ^{2} - 4 x - 4}{x ^{2} - 4 x - 5}, y = 0

6 t (\frac{d y}{d t}) + y = t^{3}

What is (\partial)/(\partial x)(sin(pixy)) ?
The answer to (\partial)/(\partial x)(sin(pixy)) is cos(pixy)piy