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

The answer to (\partial)/(\partial y)(xcos(y/z)) is -(xsin(y/z))/z

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

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

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

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (\frac{y}{z}) = \frac{1}{z}

= x (- sin (\frac{y}{z}) \frac{1}{z})

Simplify

x (- sin (\frac{y}{z}) \frac{1}{z}) : - \frac{x sin ( \frac{y}{z} )}{z}

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

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

\frac{y ^{^{'}}}{3} = x^{2} y, y (0) = - 8

x \frac{d x}{d t} + b t = 0

\frac{\partial}{\partial x} (2 y cos^{2} (x))

\int_{0}^{6} 4 x - 2 x^{2} d x

What is (\partial)/(\partial y)(xcos(y/z)) ?
The answer to (\partial)/(\partial y)(xcos(y/z)) is -(xsin(y/z))/z