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find the derivative of y with respect to x, t or theta.
(a) e^7  10x
Answer: 10e^710x
(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
 one year ago
 one year ago
find the derivative of y with respect to x, t or theta. (a) e^7  10x Answer: 10e^710x (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
 one year ago
 one year ago

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jim_thompson5910Best ResponseYou've already chosen the best response.0
The first one is \[\Large e^{710x}\] right?
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
The derivative of that isn't 10e^710x, so there has to be a typo somewhere
 one year ago

ammu123Best ResponseYou've already chosen the best response.0
im not sure i think we have to use the u substitution method to find the answer.
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
oh wait, is the answer is \[\Large 10e^{710x}\] and not \[\Large 10e^{7}10x\]
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
this is why parenthesis are useful if 710x is in the exponent, then say e^(710x)
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
ok that makes more sense now
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
let u = 7  10x, which means du/dx = 10 this means \[\Large e^{710x}\] turns into \[\Large e^{u}\] then derive to get \[\Large e^{u}*\frac{du}{dx}\] \[\Large e^{u}(10)\] \[\Large 10e^{u}\] \[\Large 10e^{710x}\]
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
I'm using the chain rule, which is If h(x) = f(g(x)), then h ' (x) = f ' (g(x)) * g ' (x)
 one year ago

ammu123Best ResponseYou've already chosen the best response.0
ok i just need help with the other 3 as well
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
whats the derivative of 8xe^x
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
use the product rule
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
tell me what you get
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
no, but that's part of it though
 one year ago

jim_thompson5910Best ResponseYou've already chosen the best response.0
Product Rule: if h(x) = f(x)*g(x), then h ' (x) = f ' (x) * g(x) + f(x) * g ' (x)
 one year ago
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