What is (\partial)/(\partial x)(xsin(3y)-ze^{-2x}) ?

The answer to (\partial)/(\partial x)(xsin(3y)-ze^{-2x}) is sin(3y)+2e^{-2x}z

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(\partial)/(\partial x)(xsin(3y)-ze^{-2x})

\frac{\partial}{\partial x} (x sin (3 y) - z e^{- 2 x})

sin (3 y) + 2 e^{- 2 x} z

Solution steps

\frac{\partial}{\partial x} (x sin (3 y) - z e^{- 2 x})

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x sin (3 y)) - \frac{\partial}{\partial x} (z e^{- 2 x})

\frac{\partial}{\partial x} (x sin (3 y)) = sin (3 y)

\frac{\partial}{\partial x} (z e^{- 2 x}) = - 2 z e^{- 2 x}

= sin (3 y) - (- 2 z e^{- 2 x})

Simplify

= sin (3 y) + 2 e^{- 2 x} z

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What is (\partial)/(\partial x)(xsin(3y)-ze^{-2x}) ?
The answer to (\partial)/(\partial x)(xsin(3y)-ze^{-2x}) is sin(3y)+2e^{-2x}z