What is (\partial)/(\partial y)(-e^{-x}sin(yz)) ?

The answer to (\partial)/(\partial y)(-e^{-x}sin(yz)) is -e^{-x}cos(yz)z

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(\partial)/(\partial y)(-e^{-x}sin(yz))

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

- e^{- x} cos (yz) z

Solution steps

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

Treat

x, z

as constants

Take the constant out:

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

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

Apply the chain rule:

cos (yz) \frac{\partial}{\partial y} (yz)

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

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

= - e^{- x} cos (yz) z

\int \frac{1}{v ^{2} + 2 v} d v

\int \frac{1}{( x ^{2} + 1 ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (- (3 x + 2) cos (2 x))

f (x) = sin (x) + \frac{1}{2} cot (x)

n = 0 \sum \infty \frac{n}{2 n + 4}

What is (\partial)/(\partial y)(-e^{-x}sin(yz)) ?
The answer to (\partial)/(\partial y)(-e^{-x}sin(yz)) is -e^{-x}cos(yz)z