What is the derivative of (a^2+x^2e^{-x^2-a^2}) ?

The derivative of (a^2+x^2e^{-x^2-a^2}) is 2e^{-x^2-a^2}x-2e^{-x^2-a^2}x(a^2+x^2)

What is the first derivative of (a^2+x^2e^{-x^2-a^2}) ?

The first derivative of (a^2+x^2e^{-x^2-a^2}) is 2e^{-x^2-a^2}x-2e^{-x^2-a^2}x(a^2+x^2)

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\frac{d}{d x} ((a^{2} + x^{2}) e^{- x^{2} - a^{2}})

2 e^{- x^{2} - a^{2}} x - 2 e^{- x^{2} - a^{2}} x (a^{2} + x^{2})

Solution steps

\frac{d}{d x} ((a^{2} + x^{2}) e^{- x^{2} - a^{2}})

Apply the Product Rule:

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

f = a^{2} + x^{2}, g = e^{- x^{2} - a^{2}}

= \frac{d}{d x} (a^{2} + x^{2}) e^{- x^{2} - a^{2}} + \frac{d}{d x} (e^{- x^{2} - a^{2}}) (a^{2} + x^{2})

\frac{d}{d x} (a^{2} + x^{2}) = 2 x

\frac{d}{d x} (e^{- x^{2} - a^{2}}) = - 2 e^{- x^{2} - a^{2}} x

= 2 x e^{- x^{2} - a^{2}} + (- 2 e^{- x^{2} - a^{2}} x) (a^{2} + x^{2})

Simplify

= 2 e^{- x^{2} - a^{2}} x - 2 e^{- x^{2} - a^{2}} x (a^{2} + x^{2})

\frac{d}{d x} (- 4 cos^{3} (x))

y = x^{2} - 2

x \to 3 lim (4)

15 x - 0.4 x^{2} - 80

\frac{\partial}{\partial x} (cos (5 x + 9 y + 7 z))

What is the derivative of (a^2+x^2e^{-x^2-a^2}) ?
The derivative of (a^2+x^2e^{-x^2-a^2}) is 2e^{-x^2-a^2}x-2e^{-x^2-a^2}x(a^2+x^2)
What is the first derivative of (a^2+x^2e^{-x^2-a^2}) ?
The first derivative of (a^2+x^2e^{-x^2-a^2}) is 2e^{-x^2-a^2}x-2e^{-x^2-a^2}x(a^2+x^2)