Find the derivative of sin x from first principle

Asked by admin @ 16/08/2021 in Math viewed by 300 People

Answered by admin @ 16/08/2021

F(x) = sin (x)
f(x+h) = sin(x+h)
From first principle,

d(f(x))/dx = lim h->0 [ f(x+h) - f(x) ] /h

Now,

d(sinx)/dx = lim h->0 sin(x+h) - sin(x) / h
= lim h->0 2 cos ( x + h/2) sin h/2 / h
= lim h->0 (2/2) (cos ( x + h/2) )* (sin h/2 / h/2)
= Lim h->0 cos ( x + h/2)
= cos x

Hence proved from first principle that
d(sin x)/dx = cos x

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