MYTUTOR SUBJECT ANSWERS

185 views

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

Sophie C. A Level Maths tutor, GCSE Maths tutor

4 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

176 SUBJECT SPECIALISTS

£20 /hr

Viktoriya L.

Degree: accounting and finance (Bachelors) - LSE University

Subjects offered: Maths, Russian+ 5 more

Maths
Russian
Mandarin
History
Economics
Accounting
-Personal Statements-

“Hello, My name is Viktoriya. I am a first year student at the London school of Economics and Poliical science studying accounting and finance. I am passionate about maths and finance in particular and wish to convey this passion to yo...”

£22 /hr

Venetia L.

Degree: General Engineering (Masters) - Durham University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“About Me: I study General Engineering at the University of Durham. I have always enjoyed the maths and science subjects, and hope to help students who also share my love for them too! I have experience in working with young pupils and...”

£20 /hr

Henry T.

Degree: Economics (Bachelors) - Leeds University

Subjects offered: Maths, Economics

Maths
Economics

“About me: I am a 20 year old third year economics student, currently achieving a first class degree at the Univesity of Leeds. Economics and Maths are two subjects that genuinely excite me. My degree allows me to study economics but al...”

MyTutor guarantee

About the author

£20 /hr

Sophie C.

Degree: Mathematics (Bachelors) - Birmingham University

Subjects offered: Maths

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

How can I improve my mathematics

If cos(x)= 1/3 and x is acute, then find tan(x).

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

A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok