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

The answer to (\partial)/(\partial x)(sin(3y)+2ze^{-2x}) is -4e^{-2x}z

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

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

- 4 e^{- 2 x} z

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (sin (3 y)) = 0

\frac{\partial}{\partial x} (2 z e^{- 2 x}) = - 4 z e^{- 2 x}

= 0 - 4 z e^{- 2 x}

Simplify

= - 4 e^{- 2 x} z

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

\int (2 x + 3) 2 x + 1 d x

\frac{d}{d x} (sech^{2} (3 x))

\int \frac{2 x - 3}{x ^{2} + 4 x + 5} d x

n = 2 \sum \infty \frac{- 1}{n}

What is (\partial)/(\partial x)(sin(3y)+2ze^{-2x}) ?
The answer to (\partial)/(\partial x)(sin(3y)+2ze^{-2x}) is -4e^{-2x}z