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

i need to know the actual rule

### 6 Answers

- Mein Hoon NaLv 71 decade agoFavorite 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

- IvanLv 51 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
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
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