## ammu123 2 years ago find the derivative of y with respect to x, t or theta. (a) e^7 - 10x (b) 8xe^x - 8e^x (c) y= (x^2 -2x+4)e^x (d) y= sin e^theta^4 please show the steps. thank you

1. cluo

what is the derivative for a constant?

2. ammu123

zero?

3. cluo

4. ammu123

is it -10?

5. cluo

yes

6. ammu123

the answer to a is -10e^7-10x

7. cluo

is that the correct answer or your?

8. ammu123

thats the correct answer but i just dont know how to get it

9. cluo

(a) should be -10

10. cluo

I think your missing some information

11. cluo

is it y = e^7 - 10x?

12. cluo

or e^(7-10x)?

13. ammu123

i think we r suppose to use the u substitution method. no the answer is -10e^7-10x

14. cluo

what is the derivative of e^x?

15. mjr632

Are you familiar with the power rule and that any derivative of a constant will equal zero? $\frac{d}{dx}(x^{n})=nx^{x-1}$

16. ammu123

yea

17. cluo

the first one should be e^(7 - 10x)

18. cluo

do you know the derivative of e^x?

19. ammu123

no is it x?

20. cluo

no it is e^x

21. cluo
22. cluo

do you know the chain rule?

23. ammu123

yes

24. cluo

okay so what is the first one?

25. cluo

You can pretend its e^u and u = 7-10x

26. ammu123

im not sure can u explain?

27. cluo

so what is the derivative of e^x?

28. ammu123

e^x

29. cluo

30. ammu123

e^u which is e^7-10x

31. cluo

right now you have to use the chain rule by taking du/dx and multiply to e^u

32. cluo

so du/dx * e^u is the answer.

33. ammu123

ok i think i got it! :)