What is (\partial)/(\partial x)(e^{-3x-y}) ?

The answer to (\partial)/(\partial x)(e^{-3x-y}) is -3e^{-3x-y}

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(\partial)/(\partial x)(e^{-3x-y})

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

- 3 e^{- 3 x - y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= e^{- 3 x - y} (- 3)

Simplify

= - 3 e^{- 3 x - y}

\frac{d}{d x} (arccos (\frac{11}{x}))

\int \frac{8 e ^{3 t}}{1 + e ^{6 t}} d t

\int \frac{x}{x ^{2} + 5} d x

y = (1 - \frac{x}{7})^{- 7}

\int \frac{1}{x ^{1.1}} d x

What is (\partial)/(\partial x)(e^{-3x-y}) ?
The answer to (\partial)/(\partial x)(e^{-3x-y}) is -3e^{-3x-y}