Find the differential of y(x)=(5x*Cos(3x))^2

Firstly I would state the substitution rule, letting 5xCos(3x)=w(x), and differentiating with respect to w(x). This gives y'(x)=2w'(x)(w(x)).I would then demonstrate the product rule stating where u and v are functions of x. That (uv)'=v'u+vu'. And apply this to the example giving w'(x)=5Cos(3x)-15xSin(3x).substituting w(x) and w'(x) back into the equation gives y'(x)=(10Cos(3x)-30xSin(3x))5xCos(3x)

Answered by Harry L. Maths tutor

3143 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Find ∫ (2x^5 - 1/(4x^3)-5) dx. giving each term in its simplest form.


What are the different steps involved in Proof by Induction?


A curve C has the following equation: x^3 + 3y - 4(x^3)*(y^3) a) Show that (1,1) lies on C b) Find dy/dx


Solve the inequality |4x-3|<|2x+1|.


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