Differentiate y=x^4sinx

  1. Firstly, we must recognise that the function is in the form of a product, y=uv, where u and v are functions of x. Therefore, we can use the product rule, dy/dx = u (dv/dx) + v (du/dx). 2) We can write u = x^4 and differentiating this we obtain du/dx = 4x^3 by multiplying by the power then taking one off the power (the general rule for differentiation being y=ax^n, dy/dx = anx^(n-1). 3) We then take v= sinx and differentiating this we obtain dv/dx = cosx. 4) The product rule then gives, dy/dx = u (dv/dx) + v (du/dx) = x^4cosx + 4x^3sinx. 5) Simplifying this then gives, dy/dx = x^3 (xcosx + 4sinx).
HM
Answered by Holly M. Maths tutor

6881 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Show that the volume of the solid formed by the curve y=cos(x/2), as it is rotated 360° around the x-axis between x= π/4 and x=3π/4, is of the form π^2/a. Find the constant a.


Rationalise the denominator of \frac{6}{\sqrt{2}}.


The curve C has the equation: 16y^3 +9x^2y-54x=0, find the x coordinates of the points on C where dy/dx = 0


Using logarithms solve 8^(2x+1) = 24 (to 3dp)


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