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

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hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1do you know the chain rule ?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0not really sure with the chain rule..

sam1194
 2 years ago
Best ResponseYou've already chosen the best response.0need to learn that then to do a question of this type

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0yes, that's why I'm trying to learn it here.. if that helps.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1let 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 ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1by definition, \(f(g(x))' = f'(g(x)) \times g'(x)\)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1so try once for your Q, maybe.. ?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0you dont subtract the exponent n1?

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1for x^n, the derivative is \((x^n)'=n x^{n1}\)

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0okay... sort of there. but then the second equation next to it confused me a little.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1yeah, 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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1in your Q, you'll multiply by (x^3+3x+8)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1**by the derivative of (x^3+3x+8)

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1no... 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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1so, 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 ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1derivative of x^3+3x+8 lets take it term by term derivative of x^3 =... ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1no... derivative of x^n = nx^{n1}

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.02? i really am so confused

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i understand that better.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0now what if 2 was plugged in

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1so, 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 ?

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

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1didn't i mention to u the chain rule ?

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0oh yeah, multiple use the one before and after

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1so any doubts now ? that would be your final answer...

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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i did but im still not sure what am i suppose to do.

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0i plug them in but i get confused with the derivative and actually multiplying it out.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.12(x^3+3x+8) * (3x^2+3) put x=2 2(2^3+3*2+8) * (3*2^2+3) =... ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.1i 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

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0thank you. thats correct

mathcalculus
 2 years ago
Best ResponseYou've already chosen the best response.0would 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.
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