Differentiating (x^2)(sinx) Using the Product Rule

Firstly, what is the product rule? What does it actually say? Well, it tells us how to differentiate a function of the form uv - the product of the functions u and v. If y = uv, the product rule says:

dy/dx = (du/dx)v + u(dv/dx)

So you differentiate the first bit, leaving the second part alone - giving you (du/dx)v. Then, you differentiate the second bit, leaving the first alone, - giving you u(dv/dx). And then you just add the two results to get dy/dx.

Let's look at applying this to the example in the question, trying to differentiate this: y = (x^2)(sinx)

We can see that y is a product of two functions, x^2 and sinx. Using the process above, we differentiate the first part, x^2, and leave sinx alone. That gives us (2x)(sinx). Then, we differentiate the second bit, sinx, and leave x^2 alone, and that gives us (x^2)(cosx). Then we just add the two together: (2x)(sinx) + (x^2)(cosx). So from that calculation we've shown that

dy/dx = (2x)(sinx) + (x^2)(cosx)

Answered by Edward M. Maths tutor

4594 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A curve has the equation x^2+2y^2=3x, by differentiating implicitly find dy/dy in terms of x and y.


Find the equation of the tangent to the curve y = 2 ln(2e - x) at the point on the curve where x = e.


Integral of (cos(x))^2 or (sin(x))^2


p(x)=2x^3 + 7x^2 + 2x - 3. (a) Use the factor theorem to prove that x + 3 is a factor of p(x). (b) Simplify the expression (2x^3 + 7x^2 + 2x - 3)/(4x^2-1), x!= +- 0.5


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