Question

Consider the function f(x)=e³ r g(x), where g(0)=-4 and gʹ(0)=7 Find f'(0)

Answer 1

To find f'(0) for the given function, we apply the Product Rule, which yields f'(0) = e^3 × 7.

Step-by-step explanation:

The student has asked to find the derivative of the function f(x) = e3 × g(x) at x = 0, given that g(0) = -4 and g'(0) = 7. To do this, we need to apply the Product Rule for differentiation, which states that the derivative of a product of two functions is f'(x)g(x) + f(x)g'(x).

First, we find the derivative of the constant e3 with respect to x, which is zero since it's a constant. Then we multiply that by g(x), and add the product of e3 and the derivative of g(x).

So, calculating f'(x) we get: f'(x) = 0 × g(x) + e3 × g'(x). Plugging in the values we have: f'(0) = e3 × 7. Therefore,

f'(0) = e3 × 7.