Use the chain rule to show that, if y = sec(x), then dy/dx = sec(x)tan(x).

First, write y in terms of cos(x). We are familiar with cos(x) and know how to differentiate it. We know that sec(x) = 1/cos(x) = (cos(x))-1.  Next, find dy/dx in terms of cos(x) and sin(x). Again, we are familiar with cos(x) and sin(x) and will be able to get the answer in terms of sec(x) and tan(x) later.  Time to use the chain rule. Multiply by the current power, reduce the current power by 1 and multiply by the differential of what is inside the brackets. Hence, we end up with: dy/dx = -1 x (cos(x))-2  x -sin(x) = sin(x)/cos(x) because the minus signs cancel each other. Finally, we know that we need to get dy/dx in terms of sec(x) and tan(x), so we need to look for a way to achieve this. We can get this by separating sin(x)/cos(x) into sin(x)/cos(x) x 1/cos(x). Using our knowledge of the definitions of sec(x) and tan(x), we can see that this is just sec(x) x tan(x), as required.

NL
Answered by Noah L. Maths tutor

15316 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The tangent to a point P (p, pi/2) on the curve x=(4y-sin2y)^2 hits the y axis at point A, find the coordinates of this point.


What is the remainder when you divide 2x^3+7x^2-4x+7 by x^2+2x-1?


i) It is given that f(x)=(-5-33x)/((1+x)(1+5x)), express f(x) in the form A/(1+x) + B/(1+5x) where A,B are integers. ii) hence express the integral of f(x) between x=3 and x=0 in the form (p/q)ln4 where p,q are integers.


How do I expand a bracket to a negative power if it doesn't start with a 1.


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning