Question

Differentiate by ab_initio method cos x​

Answer 1

Answer:

f(x) = cosx , differentiation by ab initio method implies differentiation using first principle.

Therefore , f(x+h)= cos(x+h),

f’(x)= Lt h–>0 [f(x+h) -f(x)]/h

= Lt h→0 [cos(x+h) - cosx]/h

=Lt h→0 [2sin(x+h+x)/2 *sin(x-x-h)/2]/h

=Lt h→0[ -sin(x +h/2)]* Lt h/2–>0 [sin(h/2)/h/2] as h–>0 , h/2–>0, So , Lt h/2–>0 [sin(h/2)/h/2] =0

f’(x) = -sinx * 1= - sinx