What is (\partial)/(\partial z)(xcos(y/z)) ?

The answer to (\partial)/(\partial z)(xcos(y/z)) is (xysin(y/z))/(z^2)

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(\partial)/(\partial z)(xcos(y/z))

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

\frac{x y sin ( \frac{y}{z} )}{z ^{2}}

Solution steps

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

Treat

x, y

as constants

Take the constant out:

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

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

Apply the chain rule:

- sin (\frac{y}{z}) \frac{\partial}{\partial z} (\frac{y}{z})

= - sin (\frac{y}{z}) \frac{\partial}{\partial z} (\frac{y}{z})

\frac{\partial}{\partial z} (\frac{y}{z}) = - \frac{y}{z ^{2}}

= x (- sin (\frac{y}{z}) (- \frac{y}{z ^{2}}))

Simplify

x (- sin (\frac{y}{z}) (- \frac{y}{z ^{2}})) : \frac{x y sin ( \frac{y}{z} )}{z ^{2}}

= \frac{x y sin ( \frac{y}{z} )}{z ^{2}}

\frac{d}{d x} (c_{1} e^{- 4 x} + c_{2} x e^{- 4 x})

\frac{\partial}{\partial y} (x^{4} + y^{4})

\int \frac{1}{3} sin (x) d x

\int 21 tan^{3} (θ) d θ

y^{^{'}} - \frac{4}{x} y = 4 x^{5}

What is (\partial)/(\partial z)(xcos(y/z)) ?
The answer to (\partial)/(\partial z)(xcos(y/z)) is (xysin(y/z))/(z^2)