Differentiate x^3(sinx) with respect to x

As we are differentiating a product (two things times together) we can use the product rule which is if:

                       y = u(x)v(x)

then

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

So firstly looking at our equation we need to identify u(x) and v(x). In our case

u(x) = x3 ​        and       v(x) = sinx

Now we need to differentiate both of them seperatly so (remember when we differentiate we times by the old power and then subtract a power)

du/dx = 3x​2          ​and       dv/dx = cosx

Now putting all this into the formula we have

    dy/dx = u(dv/dx) + v(du/dx)

             = x3​cosx + sinx(3x2​)

Then rearranging this we get

        dy/dx = x​3​cosx + 3x2sinx

SC
Answered by Sophie C. Maths tutor

31307 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is 'grouping' and how does it work?


How can I improve my score?


Given that 4(cosec x)^2 - (cot x)^2 = k, express sec x in terms of k.


Find the integral of (x+4)/x(2-x) .dx


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:

© 2025 by IXL Learning