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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Take the constant out:

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

= cos (yz) z \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

= cos (yz) z e^{- x} (- 1)

Simplify

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

\frac{d}{d x} (\frac{x ^{6}}{12} + \frac{1}{8 x ^{4}})

(3, - 9), (52, 1)

\int 0.5 x - 5 d x

\int_{6}^{9} \frac{y}{y ^{2} - 2 y - 3} d y

\frac{d}{d x} (3 csc (x) + 5 cos (x))

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