What is (\partial)/(\partial y)(100e^{-2x^2-y^2}) ?

The answer to (\partial)/(\partial y)(100e^{-2x^2-y^2}) is -200e^{-2x^2-y^2}y

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(\partial)/(\partial y)(100e^{-2x^2-y^2})

\frac{\partial}{\partial y} (100 e^{- 2 x^{2} - y^{2}})

- 200 e^{- 2 x^{2} - y^{2}} y

Solution steps

\frac{\partial}{\partial y} (100 e^{- 2 x^{2} - y^{2}})

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 100 \frac{\partial}{\partial y} (e^{- 2 x^{2} - y^{2}})

Apply the chain rule:

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

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

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

= 100 e^{- 2 x^{2} - y^{2}} (- 2 y)

Simplify

= - 200 e^{- 2 x^{2} - y^{2}} y

\int \frac{5 sin ^{3} ( x )}{cos ( x )} d x

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

\int (x^{8} + 1) e^{x^{9} + 9 x} d x

y^{^{''}} + 19 y = 0

x \to - 5 - lim (\frac{∣ 5 - x ∣}{5 - x})

What is (\partial)/(\partial y)(100e^{-2x^2-y^2}) ?
The answer to (\partial)/(\partial y)(100e^{-2x^2-y^2}) is -200e^{-2x^2-y^2}y