Use the chain rule to differentiate y=1/x^2-2x-1

First we will rewrite y so it is written with a power: y=1/x2-2x-1=(x2-2x-1)-1 Now let u=x2-2x-1 => du/dx = 2x -2 Writing y in terms of u: y=u-1 => dy/du= -u-2 = - 1/u2 using the chain rule: dy/dx = dy/du x du/dx =-1/ux (2x-2) substituting back in the value of u: =-(2x-2)/(x2-2x-1)= dy/dx

AP
Answered by Alicia P. Maths tutor

17911 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A ball is released on a smooth ramp at a distance of 5 metres from the ground. Calculate its speed when it reaches the bottom of the ramp.


Given that 5cos^2(x) - cos(x) = sin^2(x), find the possible values of cos(x) using a suitable quadratic equation.


Define the derivative of a function f(x) and use this to calculate the derivative of f(x)=x^n for positive integer n.


Consider the unit hyperbola, whose equation is given by x^2 - y^2 = 1. We denote the origin, (0, 0) by O. Choose any point P on the curve, and label its reflection in the x axis P'. Show that the line OP and the tangent line to P' meet at a right angle.


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:

© 2026 by IXL Learning