Question

Diffrerentiate tanx from first principle

Answer 1

I don’t know brother

Answer 2

Answer:

Step-by-step explanation:

In general, the derivative of any function say f(x) is given as

f′(x)=limh→0f(x+h)−f(x)h

∴ddx(tanx)=limh→0tan(x+h)−tan(x)h

=limh→0sin(x+h)cos(x+h)−sinxcosxh

=limh→0sin(x+h)cosx−cos(x+h)sinxhcosxcos(x+h)

=limh→0sin(x+h−x)hcosxcos(x+h)

=limh→0sinhhcosxcos(x+h)

=limh→0sinhh⋅limh→01cosxcos(x+h)

=1⋅1cosx⋅cosx

=1cos2x

=sec2x