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

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

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

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

- e^{- x - 3 y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (- x - 3 y) = - 1

= e^{- x - 3 y} (- 1)

Simplify

= - e^{- x - 3 y}

x^{2} - 6, ∣ x ∣

f (x) 5 x + y = 6

\int \frac{x}{2 - x} d x

\int tan^{5} (x) sec (x) d x

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

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