Question

Compute and simplify the derivatives of the following functions:

1. g(x)=eˣ+x²+2 x
2. f(x)=x eˣ
3. h(x)=x³ / eˣ
4. f(x)=eˣ²
5. f(x)=3 x²

Answer 1

To compute the derivatives of the given functions: g(x) = eˣ + x² + 2x, f(x) = xeˣ, h(x) = x³ / eˣ, f(x) = eˣ², and f(x) = 3x².

Step-by-step explanation:

To compute and simplify the derivatives of the given functions:

1. g(x) = eˣ + x² + 2x: The derivative of g(x) is g'(x) = eˣ + 2x + 2.
2. f(x) = xeˣ: The derivative of f(x) is f'(x) = eˣ + xeˣ.
3. h(x) = x³ / eˣ: The derivative of h(x) is h'(x) = (3x² - x³) / eˣ.
4. f(x) = eˣ²: The derivative of f(x) is f'(x) = 2xeˣ².
5. f(x) = 3x²: The derivative of f(x) is f'(x) = 6x.