DERIVATIVE OF TANX BY FIRST PRINCIPLE

Let

f(x) = tanx

Derivative of tanx using first principle :

Solved Problems

Find the derivative of each of the following.

Problem 1 :

tan(7x)

Solution :

We already know the derivative of tanx, which is sec²x. We can find the derivative of tan(7x) using chain rule.

= [tan(7x)]'

= [sec²(7x)](7x)'

= [sec²(7x)](7)

= 7sec²(7x)

Problem 2 :

tan(4x - 13)

Solution :

= [tan(4x - 13)]'

= [sec²(4x - 13)](4x - 13)'

= [sec²(4x - 13)](4 - 0)

= [sec²(4x - 13)](4)

= 4sec²(4x - 13)

Problem 3 :

tan(3x² - x + 5)

Solution :

= [tan(3x² - x + 5)]'

= [sec²(3x² - x + 5)](3x² - x + 5)'

= [sec²(3x² - x + 5)](6x - 1 + 0)

= [sec²(3x² - x + 5)](6x - 1)

= (6x - 1)sec²(3x² - x + 5)

Problem 4 :

tan²x

Solution :

= (tan²x)'

= (2tan^2-1x)(tanx)'

= (2tanx)(sec²x)

= 2tanxsec²x

Problem 5 :

Solution :

Problem 6 :

tan√x

Solution :

Problem 7 :

e^tanx

Solution :

= (e^tanx)'

= e^tanx(tanx)'

= e^tanx(sec²x)

= (sec²x)e^tanx

Problem 8 :

ln(tanx)

Solution :

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.