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kelly226Best ResponseYou've already chosen the best response.1
If the square is meant for the sin... y = sqrt x + (1/4)[sin 2x]^2 y' = (1/2)(1 / sqrt x) + (1/4)(2)(sin 2x)(cos 2x)(2) = (1 / 2 sqrt x) + (sin 2x)(cos 2x)
 one year ago

kelly226Best ResponseYou've already chosen the best response.1
If the square is only on the 2x... y = sqrt x + (1/4)sin (2x)^2 = sqrt x + (1/4) sin (4x^2) y' = (1/2)(1 / sqrt x) + (1/4)[cos (4x^2)](4*2x) = (1 / 2 sqrt x) + (2x)cos (4x^2)
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
hint : derivative of sqrt(f(x)) = 1/(f'(x)*sqrt(f(x)) and derivative of sin(g(x))=g'(x)*cos(g(x))
 one year ago

calculushelp01Best ResponseYou've already chosen the best response.0
could you step by step for the solution (the square is only on the 2x)
 one year ago

kelly226Best ResponseYou've already chosen the best response.1
If the square is only on the 2x... y = sqrt x + (1/4)sin (2x)^2 = sqrt x + (1/4) sin (4x^2) y' = (1/2)(1 / sqrt x) + (1/4)[cos (4x^2)](4*2x) = (1 / 2 sqrt x) + (2x)cos (4x^2)
 one year ago

calculushelp01Best ResponseYou've already chosen the best response.0
is the the (2x)^2 becoming (2x^2) product rule?
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
its use chain rule... derivative of (2x)^2 is 2(2x)*2
 one year ago

calculushelp01Best ResponseYou've already chosen the best response.0
wouldnt the derivative of (2x)^2 be 4x then according to chain rule= 2(2x)^21 (2)
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
but, if we look the first question there is a coefficien of sin (2x)^2 (is 1/4), so multiply it by derivative of sin (2x)^2
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
therefore, 1/4*2(2x)*2*cos(2x)^2 = 2xcos(2x)^2
 one year ago

calculushelp01Best ResponseYou've already chosen the best response.0
I understand the 2xcos part of the solution. But I dont understand why the original (2x)^2 remains
 one year ago

RadEnBest ResponseYou've already chosen the best response.0
because derivative of sin(f(x) is f'(x)*cos(f(x))
 one year ago

calculushelp01Best ResponseYou've already chosen the best response.0
oh okay thank you very much
 one year ago
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