Final answer:
The formula for the nth derivative of f(x)=7eˣ is (7eˣ)ⁿ
Step-by-step explanation:
To find the formula for the nth derivative of f(x)=7eˣ, we can use the chain rule of differentiation. The chain rule states that if y = f(g(x)), then the derivative of y with respect to x is given by dy/dx = f'(g(x)) * g'(x).
Here, g(x) = eˣ and f(g) = 7g. So, the derivative of f(g) with respect to x is df/dx = f'(g) * g'(x).
Since f'(g) = 7 and g'(x) = eˣ, substituting these values gives us the formula for the nth derivative: (7eˣ)ⁿ.