ammu123 2 years ago find the derivative of y with respect to x, t or theta. (a) e^7 - 10x Answer: -10e^7-10x (b) 8xe^x - 8e^x answer: 8xe^x (c) y= (x^2 -2x+4)e^x answer: (x^2+2)e^x (d) y= sin e^theta^4 answer: (-4theta^3 e^-theta^4) cos e^-theta^4 please show the steps. thank you

1. jim_thompson5910

The first one is $\Large e^{7-10x}$ right?

2. ammu123

yes

3. jim_thompson5910

The derivative of that isn't -10e^7-10x, so there has to be a typo somewhere

4. ammu123

im not sure i think we have to use the u substitution method to find the answer.

5. jim_thompson5910

oh wait, is the answer is $\Large -10e^{7-10x}$ and not $\Large -10e^{7}-10x$

6. ammu123

yea its the first one

7. jim_thompson5910

this is why parenthesis are useful if 7-10x is in the exponent, then say e^(7-10x)

8. jim_thompson5910

ok that makes more sense now

9. ammu123

10. jim_thompson5910

let u = 7 - 10x, which means du/dx = -10 this means $\Large e^{7-10x}$ turns into $\Large e^{u}$ then derive to get $\Large e^{u}*\frac{du}{dx}$ $\Large e^{u}(-10)$ $\Large -10e^{u}$ $\Large -10e^{7-10x}$

11. jim_thompson5910

I'm using the chain rule, which is If h(x) = f(g(x)), then h ' (x) = f ' (g(x)) * g ' (x)

12. ammu123

ok i just need help with the other 3 as well

13. jim_thompson5910

whats the derivative of 8xe^x

14. ammu123

im not sure

15. jim_thompson5910

use the product rule

16. jim_thompson5910

tell me what you get

17. ammu123

is it 8xe^x

18. jim_thompson5910

no, but that's part of it though

19. jim_thompson5910

Product Rule: if h(x) = f(x)*g(x), then h ' (x) = f ' (x) * g(x) + f(x) * g ' (x)