## lilg132 3 years ago differentiate

1. lilg132

\[M = 4.2e ^{2x} - 2.9e ^{-0.2x}\]

2. mathdood

okay well what is the derivative of e^x?

3. lilg132

xe? i dont know

4. mathdood

it is e^x*x' and the derivative of x is 1 so you have e^x but in this case since you have 2x and -0.2x you need to bring those down and differentiate you know what I mean?

5. mathdood

crazy eh derivative of e^x is e^x!!

6. lilg132

LOL

7. lilg132

no i dont explain further please :(

8. mathdood

but that it isn't the end of your problem okay do you know how to take simple derivative like x^2? like do you know the power rule?

9. lilg132

x^2 would be 2x?

10. mathdood

right just making sure.

11. mathdood

Okay so when you see e^x you have e^x and when you see e^2x you get e^2x*(2x)' the ' means derivative. You understand? If not I don't mind continuing at all.

12. lilg132

ok.. e^2x * (2x)' is e^2x

13. mathdood

no what is the derivative of 2x?

14. lilg132

x^2 ?

15. lilg132

mindboggling

16. mathdood

no that is the integral of 2x think about it like this. The derivative is the rate of change of the function so you are looking for the how fast the function is changing. so how fast is 2x changing?

17. mathdood

sorry not how fast but by how much is it changing for each value of x

18. lilg132

2?

19. lilg132

by 2?

20. mathdood

yes =) just for fun what is the derivative of 2?

21. lilg132

LOL erm not sure

22. lilg132

1?

23. lilg132

wait its a constant

24. lilg132

so 0

25. mathdood

sorry I know I am dragging this out I just want to help you understand. Well think how much is the function y=2 changing over time right!! =)

26. mathdood

0

27. mathdood

Anyway back to the problem

28. lilg132

ok :)

29. mathdood

so if (e^2x)' = 2e^2x then what do you think (4.2e^2x)' = ?

30. lilg132

8.4e^2x

31. lilg132

32. mathdood

good stuff dude now how about (−2.9e^(−0.2x))' = ?

33. mathdood

yes you got it =) keep going you can do this

34. lilg132

:D 0.58e^-0.2x?

35. mathdood

I didn't check on the calculator but it looks right dude so now you just have to put the whole thing together you want to show me what that looks like?

36. lilg132

ok one second :D

37. lilg132

dm/dx = 8.4e^2x + 0.58e^-0.2x

38. mathdood

awesome dude high five! =)

39. lilg132

woooooooooooo !!!

40. lilg132

thanks alot mate appreciate it

41. mathdood

not a problem =) thanks