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

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

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

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

- e^{- x} sin (yz)

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

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

Apply the chain rule:

e^{- x} \frac{\partial}{\partial x} (- x)

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

\frac{\partial}{\partial x} (- x) = - 1

= sin (yz) e^{- x} (- 1)

Simplify

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

\frac{d}{d x} (y cos (2 x))

f (x) = x^{3} - 3 x + 2

\int \frac{4}{16 x ^{2} + 1} d x

\int 2 e^{2 t + 5} d t

\frac{d}{d x} ((ln (3) + e^{x^{e}})^{e})

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