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can someone help me solve this problem ?
let f(x)= (x^3+3x+8)^2
F'(x)=
F'(2)=
 one year ago
 one year ago
can someone help me solve this problem ? let f(x)= (x^3+3x+8)^2 F'(x)= F'(2)=
 one year ago
 one year ago

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hartnnBest ResponseYou've already chosen the best response.1
do you know the chain rule ?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
not really sure with the chain rule..
 one year ago

sam1194Best ResponseYou've already chosen the best response.0
need to learn that then to do a question of this type
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
yes, that's why I'm trying to learn it here.. if that helps.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
let me give you a similar example, if \(f(x) = (ax^2+bx+c)^3 \) then by chain rule, \(f'(x)=3(ax^2+bx+c)^2 (ax^2+bx+c)' \\ =3(ax^2+bx+c)^2(2ax+b) \) got this ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
by definition, \(f(g(x))' = f'(g(x)) \times g'(x)\)
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
so try once for your Q, maybe.. ?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
you dont subtract the exponent n1?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
i made the exponent n1 in the Q, ax^2+bx+c had exponent 3, in the answer i became 2, right ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
for x^n, the derivative is \((x^n)'=n x^{n1}\)
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
okay... sort of there. but then the second equation next to it confused me a little.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yeah, from the definition, i needed to multiply by the derivative of inner function also (g'(x)) so ,i multiplied by derivative of ax^2+bx+c which is 2ax+b
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
in your Q, you'll multiply by (x^3+3x+8)
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
**by the derivative of (x^3+3x+8)
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
so the derivative for F'(x) would be.. (3x^2+3x+8)?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
no... you have to first derivate the out function, (x^2), then multiply the derivative of each term of x^3+3x+8 first tell whats the derivative of x^2
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
so, derivative of (x^3+3x+8)^2 will be 2(x^3+3x+8) *(derivative of x^3+3x+8 ) , right ? can you differentiate, x^3+3x+8 ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
derivative of x^3+3x+8 lets take it term by term derivative of x^3 =... ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
no... derivative of x^n = nx^{n1}
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
2? i really am so confused
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
derivative of a constant = 0 so derivative of 8 is 0 so, derivative of x^3+3x+8 = 3x^2+3 right ?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
i understand that better.
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
now what if 2 was plugged in
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
so, we have : derivative of (x^3+3x+8)^2 will be 2(x^3+3x+8) *(derivative of x^3+3x+8 ) , = 2(x^3+3x+8) * (3x^2+3) got this ?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
i thought the derivative of f '(x) is 3x^2+3
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
didn't i mention to u the chain rule ?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
oh yeah, multiple use the one before and after
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
so any doubts now ? that would be your final answer...
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
nope no doubts. now what if the problem was f ' (2)= ?
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
i did but im still not sure what am i suppose to do.
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
i plug them in but i get confused with the derivative and actually multiplying it out.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
2(x^3+3x+8) * (3x^2+3) put x=2 2(2^3+3*2+8) * (3*2^2+3) =... ?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
i get 660 :P using google https://www.google.co.in/search?q=2(2%5E3%2B3*2%2B8)+*+(3*2%5E2%2B3)&aq=f&oq=2(2%5E3%2B3*2%2B8)+*+(3*2%5E2%2B3)&aqs=chrome.0.57.192&sourceid=chrome&ie=UTF8
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
thank you. thats correct
 one year ago

mathcalculusBest ResponseYou've already chosen the best response.0
would it be possible to know the answer of a few problems because I would need to sign off and practice by hand but I would like to check my work and see if they're correct.
 one year ago
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