How do you find the derivative of #(cos x)# using the limit definition?
1 Answer
May 7, 2016
See the explanation section below.
Explanation:
We'll need the following facts:
From trigonometry:
Fundamental trigonometric limits:
And here we go:
# = lim_(hrarr0)(cosxcosh-sinxsinh-cosx)/h#
# = lim_(hrarr0)(cosxcosh-cosx-sinxsinh)/h#
# = lim_(hrarr0)((cosxcosh-cosx)/h-(sinxsinh)/h)#
# = lim_(hrarr0)(cosx(cosh-1)/h-sinx(sinh)/h)#
# = cosx(lim_(hrarr0)(cosh-1)/h)-sinx(lim_(hrarr0)(sinh)/h)#
# = cosx(0)-sinx(1)#
# = -sinx#