Question

Solve cos√x derivative by first principle_??​

Answer 1

Answer:

f′(x)=h→0limhf(x+h)−f(x)

=h→0limhcos(x+h)−cosx

=h→0lim[hcosxcosh−sinxsinh−cosx]

=h→0lim[h−cosx(1−cosh)−sinxsinh]

=h→0lim[h−cosx(1−cosh)=hsinxsinh]

=−cosx(h→0limh1−cosh)−sinxh→0lim(hsinh)

=−cosx.(0)−sinx(1)=−sinx