What is the derivative of 2xe^-x^2

Derivative of 2xe^(-x^2)

Use product rule:

y = 2xe^(-x²)

dy/dx = d/dx (2x) * e^(-x²) + 2x * d/dx (e^(-x²))
dy/dx = 2 * e^(-x²) + 2x * -2x e^(-x²)
dy/dx = 2 e^(-x²) - 4x² e(-x²)

dy/dx = 2 e^(-x²) (1 - 2x²)

In this case you need to use the chain rule and the product rule. The product rule is used inside the chain rule:
Chain rule is: f '(g(t))g'(t) - Basically you take the derivative of the outside function then the derivative of the inside function.
Product Rule: f(x)g'(x) + f '(x)g(x)

So: 2 (e^(-x^2)) + 2x(e^(-x^2)) *(-2x)

Combine and Simplify: 2(e^(-x^2)) - (4x^2) * (e^(-x^2))
Factor out the e^(-x^2) and you have the answer

Answer = e^(-x^2) * (2 - 4x^2)

Start by using product rule.
y' = 2e^(-x^2) + 2x(-2x)(e^(-x^2))
y' = 2e^(-x^2) - 4xe^(-x^2)
y' = 2e^(-x^2)(1 - 2x)