Final Answer
$-e^{\frac{-x^2}{2}}+x^2e^{\frac{-x^2}{2}}$
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Step-by-step Solution
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1
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$
$-\frac{d}{dx}\left(x\right)e^{\frac{-x^2}{2}}+x\left(-\frac{d}{dx}\left(e^{\frac{-x^2}{2}}\right)+e^{\frac{-x^2}{2}}\frac{d}{dx}\left(-1\right)\right)$
Learn how to solve product rule of differentiation problems step by step online.
$-\frac{d}{dx}\left(x\right)e^{\frac{-x^2}{2}}+x\left(-\frac{d}{dx}\left(e^{\frac{-x^2}{2}}\right)+e^{\frac{-x^2}{2}}\frac{d}{dx}\left(-1\right)\right)$
Learn how to solve product rule of differentiation problems step by step online. Find the derivative using the product rule d/dx(-xe^((-x^2)/2)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The derivative of the constant function (-1) is equal to zero. Any expression multiplied by 0 is equal to 0. x+0=x, where x is any expression.
Final Answer
$-e^{\frac{-x^2}{2}}+x^2e^{\frac{-x^2}{2}}$