Question

Solve sinx^2 by first principle method.

Answer 1

Answer:

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