Differentiate tan^2(x) with respect to x

d/dx(tan^2(x)) is not a known differential, and therefore requires a substitution to calculate it using simpler known differentials.

Using the identity sin^2(x) + cos^2(x) = 1, the equation can be divided through by cos^2(x) to give tan^2(x) + 1 = sec^2(x). Therefore tan^2(x) = sec^2(x) - 1 = 1/cos^2(x) - 1. The differential of 1 is 0, so we only need to worry about the sec^2(x) term. Using the Quotient rule, where u=1 and v=cos^2(x), d/dx(sec^2(x)) = d/dx(1/cos^2(x)) = (0 - (-2sin(x))cos(x))/cos^4(x) = 2sinx/cos^3(x).

HA
Answered by Harry A. Maths tutor

13888 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Prove: (1-cos(2A))/sin(2A) = tan(A)


Solve the equation 3x^2/3 + x^1/3 − 2 = 0


Find the differential of f(x)=y where y=3x^2+2x+4. Hence find the coordinates of the minimum point of f(x)


Find the integral on ln(x).


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences