What is (\partial}{\partial z}(xysin(\frac{piz)/3)) ?

The answer to (\partial}{\partial z}(xysin(\frac{piz)/3)) is (pixycos((piz)/3))/(3)

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(\partial}{\partial z}(xysin(\frac{piz)/3))

\frac{\partial}{\partial z} (x y sin (\frac{π z}{3}))

\frac{π x y cos ( \frac{π z}{3} )}{3}

Solution steps

\frac{\partial}{\partial z} (x y sin (\frac{π z}{3}))

Treat

x, y

as constants

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= x y \frac{\partial}{\partial z} (sin (\frac{π z}{3}))

Apply the chain rule:

cos (\frac{π z}{3}) \frac{\partial}{\partial z} (\frac{π z}{3})

= cos (\frac{π z}{3}) \frac{\partial}{\partial z} (\frac{π z}{3})

\frac{\partial}{\partial z} (\frac{π z}{3}) = \frac{π}{3}

= x y cos (\frac{π z}{3}) \frac{π}{3}

Simplify

x y cos (\frac{π z}{3}) \frac{π}{3} : \frac{π x y cos ( \frac{π z}{3} )}{3}

= \frac{π x y cos ( \frac{π z}{3} )}{3}

\frac{\partial}{\partial x} (x e^{y} - 3 yz)

\frac{3}{( x - 1 ) ^{2}}

\frac{x ^{2}}{x + 2}

\frac{d}{d x} (A x^{2} + B x)

\int cos (5 x) sin (6 x) d x

What is (\partial}{\partial z}(xysin(\frac{piz)/3)) ?
The answer to (\partial}{\partial z}(xysin(\frac{piz)/3)) is (pixycos((piz)/3))/(3)