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anonymous
 one year ago
derrivate h(t)=3e^6t*t^7*(t+6)^3
I thought it would be 18te^6t*7t^6*3(t+6)^2+t
PLEASE HELP
anonymous
 one year ago
derrivate h(t)=3e^6t*t^7*(t+6)^3 I thought it would be 18te^6t*7t^6*3(t+6)^2+t PLEASE HELP

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sweetburger
 one year ago
Best ResponseYou've already chosen the best response.0you should put parenthesis around stuff because im not sure if this all exponents to exponents

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4\[\Large\rm h(t)=3e^{6t} \cdot t^{7} \cdot (t+6)^3\]This?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4You'll have to apply your product rule, it will look kinda complicated since you have three terms though:\[\Large\rm (uvw)'=u'vw+uv'w+uvw'\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4Or you can use logarithmic differentiation if that approach I mentioned sounds too rough

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[h(t)=3e ^{6t}*t ^{7}* (t+6)^{3}\] is the equation What I thought: \[18te ^{6t}*7t ^{6}*3(t+6)^{2}+t\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok Ill use the product rule, give me just a moment, Ill try to solve it.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4Setup would look something like that I suppose :) Differentiating the blue stuff.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4ahh woops i made a boo boo ;c there we go \[\rm h'(t)=\color{royalblue}{(3e^{6t})'} \cdot t^{7} \cdot (t+6)^3\quad+\quad 3e^{6t} \cdot \color{royalblue}{(t^{7})'} \cdot (t+6)^3\]\[\rm \qquad+\quad 3e^{6t} \cdot t^{7} \cdot \color{royalblue}{((t+6)^3)'}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yup I did exactly that can I'll just write the blue on every hope u understand. The first blue would be 18e^6t, second: 7t^6. last: 3(t+6)+t. I just putthem together with the black, but that answer doesnt match the one in my book, why they gotta always mess things up....I follow their rules and stuff they never follow their own.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0opps last one, (3(t+6)^2)+t

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4woops, last blue should give us this:\[\Large\rm \color{royalblue}{\frac{d}{dx}(t+6)^3}=3(t+6)^2\color{royalblue}{(t+6)'}=3(t+6)(1)\]ya?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4Derivative of t+6 = 1+0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes ofc, silly misstake.their answer tho is: \[6te^{6t}*(t+6)^{2}*(3t ^{2}+13t21)\] HOW?!

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4We have to do some factoring :) Books tends to over simplify, sall good, we can get there.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4So what does everything have? They each have the exponential, ya? How many t's do they all have? Well they all have at least 6 t's multiplying. t^6 And they all have a factor of 3, right? :d See where we're going with this?

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4We want to pull out the greatest common factor that each term shares.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.4dw:1434882683506:dwSo we pull that out.