Question

Find the derivative of Sinx using definition of derivative

Answer 1

that's a little long and you got to know some identities.

Answer 2

=lim(h->0) (sin(x+h) - sinx)/h

=lim(h->0) (2cos(x+h/2) *sin(h/2))/h
=lim(h->0) (cos(x+h/2) *sin(h/2))/h/2
=lim(h->0)(cos(x+h/2) * lim(h/2->0) sin(h/2))/h/2
=lim(h->0)(cos(x+h/2)*1 [lim(h/2->0) sin(h/2))/h/2 =1 ]
=cosx

Answer 3

much appreciated thanks

Answer 4

welcome