What is (\partial)/(\partial x)(e^{-9x^2-2y^2}) ?

The answer to (\partial)/(\partial x)(e^{-9x^2-2y^2}) is -18e^{-9x^2-2y^2}x

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(\partial)/(\partial x)(e^{-9x^2-2y^2})

\frac{\partial}{\partial x} (e^{- 9 x^{2} - 2 y^{2}})

- 18 e^{- 9 x^{2} - 2 y^{2}} x

Solution steps

\frac{\partial}{\partial x} (e^{- 9 x^{2} - 2 y^{2}})

Treat

y

as a constant

Apply the chain rule:

e^{- 9 x^{2} - 2 y^{2}} \frac{\partial}{\partial x} (- 9 x^{2} - 2 y^{2})

= e^{- 9 x^{2} - 2 y^{2}} \frac{\partial}{\partial x} (- 9 x^{2} - 2 y^{2})

\frac{\partial}{\partial x} (- 9 x^{2} - 2 y^{2}) = - 18 x

= e^{- 9 x^{2} - 2 y^{2}} (- 18 x)

Simplify

= - 18 e^{- 9 x^{2} - 2 y^{2}} x

\int sec^{2} (2 x y) d x

\frac{d}{d x} (\frac{x ^{2} - 8 x + 7}{x ^{2} + 9})

\frac{\partial}{\partial x} (t^{2} e^{x} + 3 x^{2})

\int_{2}^{7} 3 d x

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

What is (\partial)/(\partial x)(e^{-9x^2-2y^2}) ?
The answer to (\partial)/(\partial x)(e^{-9x^2-2y^2}) is -18e^{-9x^2-2y^2}x