it is cosx.........derived from a formula
cos (x) is the answer.
Though u learn it as a formula .If u differentiate the sin x Taylor series expansion u get back the cos x Taylor series expansion.
you can solve it using first principles of differnciation
answer is cos x
Hope you know the first principle of differentiation..........
Anyways we'll take it one more time.....it is
f'(x) = Lt (h->0 ) [ f(x+h)-f(x) ] / h
You can drive this equation from the slope formula ie slope m = y2-y1 / x2-x1 in the above eq. h is x2-x1 and y2 - y1 is f(x+h) - f(h) and f'(x) is the slope of curve ie dy/dx or 'm'........
for More info read ur txt books or ping people here again............
Coming to ur ques. now substitute sin for f in the abov eq.....
Lt h->0 sin(x+h)-sinx / h
but sin(x+h)-sinx = 2 cos(x + h/2) sin (h/2)
now substituing the limits ie sin h/2 /h/2 =1
then h=0 gives "cosx" as the answer ie the derivative
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