How do you differentiate (2x+xe^6x)/(9x-(2x^2)-ln(x)) w.r.t. x?

This problem requires using the quotient rule, product rule and the chain rule. The derivative of the entire thing is ((du/dx)v-(dv/dx)u)/v^2 where u=2x+xe^6x and v=9x-2x^2-lnx. dv/dx is relatively straitforward: 9-4x-(1/x). 2x+xe^6x is less so, because this requires differentiating xe^6x. First notice this is two functions of x times each other, so we can use the product rule: so d/dx(xe^6x)=x(d/dx(e^6x))+e^6x. What is d/dx(e^6x)? We have to use the chain rule here: suppose g=6x, hence d/dg(e^g)xdg/dx=d(e^6x)=6e^6x. So now combining this altogether we know the derivative of the entire thing: ((2+e^6x+xe^6x)(9x-2x^2-lnx)-(2x+xe^6x)(9-4x-1/x))/(9x-2x^2-lnx)^2

SH
Answered by Seth H. Maths tutor

3022 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve has equation y = 20x −x^2 −2x^3 . Find its stationary point(s).


Prove by induction that the nth triangle number is given by n(n+1)/2


A triangle has sides A, B and C. The side BC has length 20cm, the angle ABC is 50 deg and angle BAC is 68 deg. a) Show that the length of AC is 16.5cm, correct to three significant figures. b) The midpoint of BC is M, hence find the length of AM


Calculate the binomial expansion of (2x+6)^5 up to x^3 where x is decreasing.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences