Question

Calculus Help Show that one function is not an antiderivative of another

Answer 1

Just differentiate G and H :

• dG/dx = d(x ² eˣ )/dx = 2x eˣ + x ² eˣ

so G is not an antiderivative of f.

• dH/dx = d(2x eˣ - 2eˣ ) = (2eˣ + 2x eˣ ) - 2eˣ = 2x eˣ = f(x)

so H is indeed an antiderivative of f.