What is (\partial)/(\partial x)(-10e^{-5x^2-y^2}x) ?

The answer to (\partial)/(\partial x)(-10e^{-5x^2-y^2}x) is -10(-10e^{-5x^2-y^2}x^2+e^{-5x^2-y^2})

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(\partial)/(\partial x)(-10e^{-5x^2-y^2}x)

\frac{\partial}{\partial x} (- 10 e^{- 5 x^{2} - y^{2}} x)

- 10 (- 10 e^{- 5 x^{2} - y^{2}} x^{2} + e^{- 5 x^{2} - y^{2}})

Solution steps

\frac{\partial}{\partial x} (- 10 e^{- 5 x^{2} - y^{2}} x)

Treat

y

as a constant

Take the constant out:

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

= - 10 \frac{\partial}{\partial x} (e^{- 5 x^{2} - y^{2}} x)

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- 5 x^{2} - y^{2}}, g = x

= - 10 (\frac{\partial}{\partial x} (e^{- 5 x^{2} - y^{2}}) x + \frac{\partial}{\partial x} (x) e^{- 5 x^{2} - y^{2}})

\frac{\partial}{\partial x} (e^{- 5 x^{2} - y^{2}}) = - 10 e^{- 5 x^{2} - y^{2}} x

\frac{\partial}{\partial x} (x) = 1

= - 10 ((- 10 e^{- 5 x^{2} - y^{2}} x) x + 1 \cdot e^{- 5 x^{2} - y^{2}})

Simplify

- 10 ((- 10 e^{- 5 x^{2} - y^{2}} x) x + 1 \cdot e^{- 5 x^{2} - y^{2}}) : - 10 (- 10 e^{- 5 x^{2} - y^{2}} x^{2} + e^{- 5 x^{2} - y^{2}})

= - 10 (- 10 e^{- 5 x^{2} - y^{2}} x^{2} + e^{- 5 x^{2} - y^{2}})

What is (\partial)/(\partial x)(-10e^{-5x^2-y^2}x) ?
The answer to (\partial)/(\partial x)(-10e^{-5x^2-y^2}x) is -10(-10e^{-5x^2-y^2}x^2+e^{-5x^2-y^2})