Could you please show work so I can understand how you got the answer

1. Set f(x) = e^3x + e^-3x . Find the rate of change of f with respect to x.

2. Set f(x) = 3e^x 3e^-x . Find the rate of change of f with respect to x.

3. Set g(x) = e^5x + ln(5x). Find the rate of change of g with respect to x.

4. Set g(x) = e^-6x + 5 ln(x). Find the rate of change of g with respect to x

5. Find the rate of change of f(x) = x⁴e^x with respect to x.

6. Calculate the rate of change of f(x) = x ln(x) with respect to x.

7. Calculate the rate of change of f(x) = e^{x^2} with respect to x.

8. Calculate the rate of change of f(x) = e^{x^3} with respect to x.

9. Calculate the rate of change of f(x) = e^{x^5} with respect to x.

10. Calculate the rate of change of h(x) = ln(x) e^{x^2} with respect to x.

11. Set f(x) = (e^x + e^-x)³ Calculate the rate of change of f with respect to x.