What is (\partial)/(\partial y)(-5e^xcos(yz)) ?

The answer to (\partial)/(\partial y)(-5e^xcos(yz)) is 5e^xzsin(yz)

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(\partial)/(\partial y)(-5e^xcos(yz))

\frac{\partial}{\partial y} (- 5 e^{x} cos (yz))

5 e^{x} z sin (yz)

Solution steps

\frac{\partial}{\partial y} (- 5 e^{x} cos (yz))

Treat

x, z

as constants

Take the constant out:

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

= - 5 e^{x} \frac{\partial}{\partial y} (cos (yz))

Apply the chain rule:

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

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

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

= - 5 e^{x} (- sin (yz) z)

Simplify

= 5 e^{x} z sin (yz)

\int \frac{a}{2} x + \frac{a}{2} d x

x \to 8 lim (2 x - 7 x^{2})

\frac{d}{d x} (\frac{x + y}{x - y})

f (x) = x^{4} - 18 x^{2} + 81, at x = 1

\frac{\partial}{\partial x} (2 y^{3} x)

What is (\partial)/(\partial y)(-5e^xcos(yz)) ?
The answer to (\partial)/(\partial y)(-5e^xcos(yz)) is 5e^xzsin(yz)