find two derivative of f(x)= e^x^(2)?

Answer 1

Second derivative?

Well the first dervative is just by chain rule (e^(x^2)*2x) and then for the second derivative use the product rule and get (e^(x^2)*2+(2x)*e^(x^2)*2x)

That may be confusing typed out like that, but remember the product rule is the first times the derivative of the second plus the second times the derivative of the first.

Answer 2

By saying, "Find two derivative," I assume you mean "find the second derivative."

f(x) = e^(2x)

Let u = 2x

du = 2 dx

f(u) = e^u

f'(u) = e^u du

f'(x) = 2 e^(2x)

f'(u) = 2 e^u

f''(u) = 2 e^u du

f''(x) = 4 e^(2x)

Answer 3

chian rule:
let u = x^2
then d/du (e^u) = e^u

d/dx (x^2) = 2x

f'(x) = e^x^2 * 2x <== answer

edit: i assumed you meant find the first derivative. if you want to find second deriative, use product rule
d/dx (uv) = u'v + v'u

Answer 4

Chain rule
let y = e^u where u = x^2. Then
dy/du =(dy*du)/(du*dx) = e^u.2x = 2xe^x^2

Answer 5

f(x) = e^(x²)
f'(x) = e^(x²) d/dx(x²) = 2xe^(x²)
f"(x) = 2e^(x²) + 2x d/dx(e^(x²)) = 2e^(x²) + 2x(2xe^(x²)) using product differentiation rule. Simplifying

f"(x) = 2e^(x²) [1 + 2x²]