How do you find the derivative of y = tan(x) using first principle?

We know that

tan(x) = sin(x) / cos(x)

d/dx tan(x) = d/dx sin(x) / cos(x)

Now will us the quotient rule for the above equation

=(cos(x) (d/dx) sin(x) – sin(x) (d-dx) cos(x) ) / cos2(x) { (d/dx) sin(x) = cos(x); (d/dx) cos(x) = -sin(x)}

=(cos(x)cos(x) + sin(x)sin(x) ) / cos2(x)

= cos2(x) + sin2(x) / cos2(x) { By trignometric identity cos2(x) + sin2(x)=1}

= 1 / cos2(x)

=sec2(x) { 1/cos2(x) = sec2(x) }

Answer

Derivative of tan x = sec2(x)

Leave a Comment

Your email address will not be published. Required fields are marked *

BOOK

Free Class