What is (\partial)/(\partial x)(e^{-8x^2-5y^2}) ?

The answer to (\partial)/(\partial x)(e^{-8x^2-5y^2}) is -16e^{-8x^2-5y^2}x

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(\partial)/(\partial x)(e^{-8x^2-5y^2})

\frac{\partial}{\partial x} (e^{- 8 x^{2} - 5 y^{2}})

- 16 e^{- 8 x^{2} - 5 y^{2}} x

Solution steps

\frac{\partial}{\partial x} (e^{- 8 x^{2} - 5 y^{2}})

Treat

y

as a constant

Apply the chain rule:

e^{- 8 x^{2} - 5 y^{2}} \frac{\partial}{\partial x} (- 8 x^{2} - 5 y^{2})

= e^{- 8 x^{2} - 5 y^{2}} \frac{\partial}{\partial x} (- 8 x^{2} - 5 y^{2})

\frac{\partial}{\partial x} (- 8 x^{2} - 5 y^{2}) = - 16 x

= e^{- 8 x^{2} - 5 y^{2}} (- 16 x)

Simplify

= - 16 e^{- 8 x^{2} - 5 y^{2}} x

n = 0 \sum \infty - \frac{1}{n + 1}

\int e^{3 x} (sin (3 x) + cos (3 x)) d x

\int (x^{2} - \frac{3}{x}) d x

n = 0 \sum \infty \frac{1}{3 n}

y = \frac{( 3 x - 6 )}{( x ^{2} + 4 )}

What is (\partial)/(\partial x)(e^{-8x^2-5y^2}) ?
The answer to (\partial)/(\partial x)(e^{-8x^2-5y^2}) is -16e^{-8x^2-5y^2}x