Question

show the differentiation rule for: (cosx)' = -sinx for any x answer asap please @Mathematics

Answer 1

lim(h-->0) (cos(x+h) - cosx)/h
= lim(h-->0) (cosxcosh - sinxsinh - cosx)/h
= lim(h-->0) ((cosxcosh-cosx)/h - sinxsinh/h)
= lim(h-->0) cosx(cosh-1/h) - sinx(sinh/h))
= cosx(0) - sinx(1)
= -sinx

Answer 2

cosh = 1 when h = 0
1-1 = 0
0/0 =0

Also, sinh/h = 1

Answer 3

when h = 0