Answer: [tex]-2xe^{-x^2}[/tex]
Step-by-step explanation:
Let u be a differentiable function , then
[tex]\dfrac{d}{dx}(e^x)=e^x[/tex]
[tex]\dfrac{d}{dx}e^u=e^u\dfrac{du}{dx}[/tex] (1)
Given function : [tex]y = e^{-x^2}[/tex]
Differentiate both sides with respect to x , we get
[tex]y'=e^{-x^2}\dfrac{d(-x^2)}{dx}[/tex] (By using (1))
[tex]\Rightarrow\ y'=e^{-x^2}(-2x)[/tex] [∵ [tex]\dfrac{d}{dx}(x^n)=x^{n-1}[/tex]]
[tex]\Rightarrow\ y'=-2xe^{-x^2}[/tex]
Hence, the derivative of the given function is [tex]-2xe^{-x^2}[/tex] .
