Answer: [tex]8xe^{x^2[/tex]
Step-by-step explanation:
Properties of derivative :
1) [tex]\dfrac{d}{dx}(e^x)=e^x[/tex]
2) [tex]\dfrac{d}{dx}(x^n)=x^{n-1}[/tex]
3) [tex]\dfrac{d}{dx}(ax)=a[/tex]
Let g be a differentiable function , then
4) [tex]\dfrac{d}{dx}e^g=e^g\dfrac{dg}{dx}[/tex]
Given function : [tex]y = 4e^{x^2}[/tex]
Differentiate both sides with respect to x , we get
[tex]y'=4e^{x^2}\dfrac{d(x^2)}{dx}[/tex] (By (4))
[tex]\Rightarrow\ y'=4e^{x^2}(2x)[/tex] (By (2))
[tex]\Rightarrow\ y'=8xe^{x^2}[/tex]
Hence, the derivative of the given function is [tex]8xe^{x^2[/tex] .
