Question

Find the derivative of cosx using first principle
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Answer 1

Answer:

The first principle states that

f'(x) = lim h->0 f(x+h)-f(x)/h

So, to find the derivative of

f(x) = cos x

Let's apply this principle for the single variable function cos x

So, we get,

f'(x) = Lim h->0. cos(x+h)-cos x / h

By the formula of

cos A - cos B = 2 sin (B-A)/2 sin (A+B/2)

We get,

f'(x) = Lim h->0 2 sin (-h/2) sin (x+h/2) / h

=>

f'(x) = - Lim h->0. sin(x+h/2) * sin(h/2)/h/2

= - sin x

Hope this helps you !

Answer 2

Answer:

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