Question:
find the derivative of cos x^2 by first principle
Answer:
Let y = cos2 x
Now, dy/dx = limh->0 {cos2 (x + h) - cos2 x}/h
=> dy/dx = limh->0 {1 - sin2 (x + h) - (1 - sin2 x)}/h
=> dy/dx = limh->0 {1 - sin2 (x + h) - 1 + sin2 x)}/h
=> dy/dx = limh->0 {sin2 x - sin2 (x + h)}/h
=> dy/dx = limh->0 {sin (x+h-x) * sin (x-x-h)}/h
=> dy/dx = limh->0 {sin (2x+h) * sin (-h)}/h
=> dy/dx = limh->0 sin (2x+h) * limh->0 sin (-h)/h
=> dy/dx = -limh->0 sin (2x+h) * limh->0 sin h /h
=> dy/dx = -sin 2x * 1
=> dy/dx = -sin2x
=> dy/dx = -2*sin x * cos x
Not what you are looking for? Go ahead and submit the question, we will get back to you.
