Question

Find the value of f ′(0) for f(x) = sin(x) + ex.

Answer 1

The value of f'(0) for the function f(x) = sin(x) + e^x is 2. This is calculated by taking the derivative of the function, which is cos(x) + e^x, and evaluating it at x=0.

Step-by-step explanation:

To find the value of f ′(0) for f(x) = sin(x) + ex, we need to calculate the derivative of the function and evaluate it at x=0. The derivative of sin(x) is cos(x), and the derivative of ex is ex. So the derivative of f(x) is:

f ′(x) = cos(x) + ex

Now we evaluate the derivative at x=0:

f ′(0) = cos(0) + e0

f ′(0) = 1 + 1

f ′(0) = 2

The value of f ′(0) is therefore 2.