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calculushelp01
 3 years ago
derivative of sqrt x + (1/4) sin (2x)^2
calculushelp01
 3 years ago
derivative of sqrt x + (1/4) sin (2x)^2

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kelly226
 3 years ago
Best ResponseYou've already chosen the best response.1If 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)

kelly226
 3 years ago
Best ResponseYou've already chosen the best response.1If 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)

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

calculushelp01
 3 years ago
Best ResponseYou've already chosen the best response.0could you step by step for the solution (the square is only on the 2x)

kelly226
 3 years ago
Best ResponseYou've already chosen the best response.1If 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)

calculushelp01
 3 years ago
Best ResponseYou've already chosen the best response.0is the the (2x)^2 becoming (2x^2) product rule?

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0its use chain rule... derivative of (2x)^2 is 2(2x)*2

calculushelp01
 3 years ago
Best ResponseYou've already chosen the best response.0wouldnt the derivative of (2x)^2 be 4x then according to chain rule= 2(2x)^21 (2)

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0but, 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

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0therefore, 1/4*2(2x)*2*cos(2x)^2 = 2xcos(2x)^2

calculushelp01
 3 years ago
Best ResponseYou've already chosen the best response.0I understand the 2xcos part of the solution. But I dont understand why the original (2x)^2 remains

RadEn
 3 years ago
Best ResponseYou've already chosen the best response.0because derivative of sin(f(x) is f'(x)*cos(f(x))

calculushelp01
 3 years ago
Best ResponseYou've already chosen the best response.0oh okay thank you very much
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