Question

differentiation of sin x by ab initio method

Answer 1

sinx=sinx.1
d(sinx.1)/dx=1.{d (sinx)/dx}+sinx. {d1/dx}
because constant differentiation is zero
so, cosx is answer

Answer 2

Answer:

d/dx sinx = cos x

Explanation:

Now by ab initio method

f(x)=sin x

and the following steps which involves in the differentiation are given on the picture with the solution.

The last  answer is  not in the solution part of the picture so it is left so,

after the last step we get

f ' ( x )= 0+ (cos x)(1 ) = cos x

Hence, the solution to the problem is

d/dx sinx = cos x