What is (\partial)/(\partial x)(e^{-4x-x^2+2y-y^2}) ?

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

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(\partial)/(\partial x)(e^{-4x-x^2+2y-y^2})

\frac{\partial}{\partial x} (e^{- 4 x - x^{2} + 2 y - y^{2}})

e^{- 4 x - x^{2} + 2 y - y^{2}} (- 2 x - 4)

Solution steps

\frac{\partial}{\partial x} (e^{- 4 x - x^{2} + 2 y - y^{2}})

Treat

y

as a constant

Apply the chain rule:

e^{- 4 x - x^{2} + 2 y - y^{2}} \frac{\partial}{\partial x} (- 4 x - x^{2} + 2 y - y^{2})

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

\frac{\partial}{\partial x} (- 4 x - x^{2} + 2 y - y^{2}) = - 2 x - 4

= e^{- 4 x - x^{2} + 2 y - y^{2}} (- 2 x - 4)

\frac{1}{x + 2}

x \to + 0 + lim (\frac{x ^{2}}{6} - \frac{5}{x})

\frac{d}{d x} ((x^{3} + 6) e^{x})

\frac{d}{d x} (sinh (0))

f (x) = x^{2}, at x = 3, x = 7

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