What is (\partial)/(\partial z)(x^2ycos(z/t)) ?

The answer to (\partial)/(\partial z)(x^2ycos(z/t)) is -(x^2ysin(z/t))/t

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(\partial)/(\partial z)(x^2ycos(z/t))

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

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

Solution steps

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

Treat

x, y, t

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= x^{2} y (- sin (\frac{z}{t}) \frac{1}{t})

Simplify

x^{2} y (- sin (\frac{z}{t}) \frac{1}{t}) : - \frac{x ^{2} y sin ( \frac{z}{t} )}{t}

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

\int 1 - (x - 1)^{2} d x

\frac{d}{d x} (x^{3} - 12 x + 1)

n = 1 \sum \infty (- 0.2)^{n}

2 cos (2 t + \frac{π}{6})

f (x) =, x at x

What is (\partial)/(\partial z)(x^2ycos(z/t)) ?
The answer to (\partial)/(\partial z)(x^2ycos(z/t)) is -(x^2ysin(z/t))/t