how do i find the derivative of "1/2 sin x" ?

i need to know the actual rule

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  • 1 decade ago
    Favorite Answer

    In case you want you want to use formula

    d/dx(mf(x)) = m d/dxf(x) when m is a constant

    d/dx (sin x) = cos x

    now apply

    d/dx((1/2) sin x = 1/2 d/dx(sin x) = (1/2) cos x

    in case you want to derive from 1st principle

    of sin x

    sin (x+h) = sin x cos h + cos x sin h

    sin (x+h) -sin x = sin x (cos h-1) + cos x sin h

    devide by h and limit as h->0

    limit of 1st term = sin x(cosh -1)/h = 0

    limit of 2nd term = cos x sinh /h = cos x

    so derivative = cos x

  • Ivan
    Lv 5
    1 decade ago

    You take the derivative of sin x which is cos x and multiply the 1/2 on it...

    So the answer is 1/2 cos x

  • 1 decade ago

    The rulw is d/dx sin x =cos x so

    d/dx 1/2 sin x= 1/2 cos x

  • 1 decade ago

    assuming that (1/2) is in brackets, so its not 1/(2sinx)

    the rule:

    the derivative of sin x is cos x

    so you leave the constant where is, the derivative will be 1/2 cos x

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  • 1 decade ago

    1/2 cos x

  • 1 decade ago

    You need to use the product rule, which states

    d/dx (fg)=f'g+fg'

    In this case, if f=1/2, f'=0 (from the power rule). If g=sinx, g'=cosx (by definition).

    Then,

    d/dx(fg) = f'g+fg' = (0)(cosx)+(1/2)(sinx) = 1/2sinx

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