Second Derivative?

Question

Can Anyone tell me how to find the second derivative of x^2*e^19x?

Answer 1

by finding the first derivative, and then finding the derivative of that

f = x^2*e^19x
f' = 2x*e^19x + 19x^2*e^19x
f'' = 2*e^19x + 38x*e^19x + 38x*e^19x + 361x^2*e^19x =
e^19x (2 + 76x + 361x^2)

Answer 2

f(x) = x^2e^(19x)

f'(x) = 2x e^(19x) + x^2 * 19 e^(19x) = e^(19x) (2x + 19x^2)

f''(x) = 19 e^(19x) (2x + 19x^2) + e^(19x) (2 + 38 x) =>
f''(x) = e^(19x) (38 x + 361x^2 + 2 + 38x) =>
f''(x) = e^(19x) (361x^2 + 76x +2)