δx = x-a

F'(a) is defined by the following derivative.

f '(a)= lim[f(a+δx)-f(a)]/δx = lim[f(a+x-a)-f(a)]/(x-a)= lim[f(x)-f(a)]/(x-a)

result

If you sign

Said.

(2) On the sinx derivative problem

sin(x+h)-sinx

Go to the next step 2cos(x+h/2)sinh/2.

use

Sum difference product

(sinh/2)/(h/2) disappears.

When x approaches 0, limsinx/x= 1 is at two important limits.

Meanwhile, for limcos(x+h/2)=cosx.

This simplification uses the definition of functional continuity.

Please adopt

thank you