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onegirl
 2 years ago
Find the indicated derivative of the function f(x) = cosx^2, find f''(x)
onegirl
 2 years ago
Find the indicated derivative of the function f(x) = cosx^2, find f''(x)

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satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0\[2\cos(x)\sin(x)\]is your first derivative take the derivative of that one, using the product rule

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0@satellite73 it will be 2cos(x)sin(x)

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0@genius12 so the derivative of 2cos(x) sin(x) , and i got 2 cos(2x)

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0@jazy should i now take the derivative of 2 cos(2x) ? or

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0which one : dw:1362427439289:dw

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0so, the first one in my diagram ?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0oke, to get the first derivative of f(x) we can use the cain rule hint : derivative of x^2 = 2x derivative of cos =  sin

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0yea i got it the first derivative will be 2 cos(x) sin (x) right?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0so, derivative of f(x) = cosx^2 > f ' (x) = 2x(sinx^2) = 2x sinx^2

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0so then i take the derivative of 2x sinx^2 ?

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0okay after i take the derivative of 2x sinx i get 2 cos(2x) so then i take the derivative of 2 cos(2x) right?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0use the product rule to get the 2nd derivative : use the formula : f '' = u'v + uv' assuming that u=2x > u' = ... ? v = sinx^2 > v ' = ... ?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0do u know derivative of 2x ?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0yes, that's right also, sinx^2 ?

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0but where does sinx^2 come from i got 2 cos(x) sin(x) ??

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0for my derivative of cosx^2

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0f(x) = cosx^2 > f ' (x) = 2x(sinx^2) = 2x sinx^2

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0it just the first derivative of f(x), now we have to deriv again to get f " then, use the product rule

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0so now i need to find the derivative of sin^x right? since we found 2x which we got 2

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0and i got cos (x) sin(x)

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0so it will be 2 cos(x) sin(x) right?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.02x sinx^2 let u=2x > u' = 2 v = sinx^2 > v ' = 2xcoscx^2

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0sorry, it should v' = 2xcosx^2

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0okay so how would i set it up in the formula ?

RadEn
 2 years ago
Best ResponseYou've already chosen the best response.0f " = u'v + uv' f " = (2)sinx^2 + (2x)2xcosx^2 = 2sinx^2  4x^2cosx^2

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0okay so the f'''(x) will be 2sinx^2 = 4x^2 cosx^2 ?

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0@RadEn so thats the final answer?
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