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)


                  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

Sophie C. A Level Maths tutor, GCSE Maths tutor

8 months ago

Answered by Sophie, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


Charley H. A Level Maths tutor, GCSE Maths tutor, A Level Economics t...
£20 /hr

Charley H.

Degree: Mathematics and Economics (Bachelors) - Liverpool University

Subjects offered:Maths, Economics


“About Myself: I am currently studying Mathematics and Economics at The University of Liverpool. I have always enjoyed these two subjects, especially maths, and I hope I can help in assisting you achieve your goal- whether that be pass...”

£20 /hr

Matthew M.

Degree: Engineering Mathematics (Bachelors) - Bristol University

Subjects offered:Maths, Law+ 1 more


“I am an Engineering Math student at the University of Bristol. I have a range of interests, which cover maths, history and law, and would love to help others in these areas as well as encourage the same enthusiasm I have in others! I a...”

MyTutor guarantee

£20 /hr

Michael O.

Degree: MSci Theoretical Physics (Masters) - Birmingham University

Subjects offered:Maths, Physics+ 2 more

Further Mathematics
-Personal Statements-

“I'm a Theoretical Physics student at the University of Birmingham. In my eyes, our goal as Physicists is to understand everything and anything that the universe presents us with, and as such, is a subject which brings together so many...”

About the author

£20 /hr

Sophie C.

Degree: Mathematics (Bachelors) - Birmingham University

Subjects offered:Maths


“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Posts by Sophie

Differentiate x^3(sinx) with respect to x

Solve 2x + 10 = 4x + 6

Other A Level Maths questions

Find the cartesian equation of a curve?

How can I find the area under the graph of y = f(x) between x = a and x = b?

how do integrate an equation with a surd or a fraction?

(Using the Quotient Rule) -> Show that the derivative of (cosx)/(sinx) is (-1)/(sinx).

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss