ammu123
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
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cluo
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what is the derivative for a constant?
ammu123
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zero?
cluo
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yeah what about -10x?
ammu123
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is it -10?
cluo
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yes
ammu123
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the answer to a is -10e^7-10x
cluo
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is that the correct answer or your?
ammu123
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thats the correct answer but i just dont know how to get it
cluo
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(a) should be -10
cluo
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I think your missing some information
cluo
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is it y = e^7 - 10x?
cluo
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or e^(7-10x)?
ammu123
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i think we r suppose to use the u substitution method. no the answer is -10e^7-10x
cluo
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what is the derivative of e^x?
mjr632
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Are you familiar with the power rule and that any derivative of a constant will equal zero? \[\frac{d}{dx}(x^{n})=nx^{x-1}\]
ammu123
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yea
cluo
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the first one should be e^(7 - 10x)
cluo
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do you know the derivative of e^x?
ammu123
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no is it x?
cluo
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no it is e^x
cluo
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do you know the chain rule?
ammu123
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yes
cluo
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okay so what is the first one?
cluo
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You can pretend its e^u and u = 7-10x
ammu123
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im not sure can u explain?
cluo
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so what is the derivative of e^x?
ammu123
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e^x
cluo
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right what about e^u?
ammu123
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e^u which is e^7-10x
cluo
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right now you have to use the chain rule by taking du/dx and multiply to e^u
cluo
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so du/dx * e^u is the answer.
ammu123
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ok i think i got it! :)