CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Using first principle, find the derivative of tanx.


Solution

Let f(x)=tanx

By using first principle, f(x)=limh0f(x+h)f(x)h

=limh0tanx+htanxh

=limh0sinx+hcosx+hsinxcosxh

=limh0sinx+hcosxsinx cosx+hh cos (x+h)cos x

=limh0sin(x+h)xh cosx cos((x+h))        [sin A cos Bcos A sin B =(AB)]

=limh0sin(x+hx)h cosx cos(x+h)×x+hxx+hx

[multipying numerator and denominator by z+hx]

=limh0x+hxxh cos x cos(x+h)×=limh0(sin(x+hx)x+hx)

=1cos2x×=limh0x+hxh×1         [=limh0sin hh=1]

=sec2x×=limh0x+hxh×x=h+xx+h+x=sec2x×=limh0x+hxh(x+h+x)

=sec2x×=limh0hh(x+h)+x

=sec2x×12x=sec2x2x

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image