How do i differentiate the equation y = x^2 + 6x + 2 with respect to x.

So lets have a quick recap of differenciation to start off. In informal terms, differenciation is carried out by dropping the power to be in front of the term we are differenciating to as well as decrementing the power. So in practice, x^3 would differenciate to 3x^2 when differenciating in terms of x.

We drop the power (being 3) so that it is in front of the term (3x). Then decrement the power (so x^3 becomes x^2). Putting it all together, we get the result 3x^2. Similarly, if we were to differenciate 2x^3. We would obtain (2)(3)x^2 being 6x^2. Don't forget to multiply your result by the number that was in front previously! Which in this case was 2 being in front of x.

Now lets look at the question in hand, lets differenciate each term separately and add them up.

1. x^2 would become 2x^1 if we were to drop the power and decrement the power. 2x^1 is easily rewritten as 2x

2. 6x. This is actually 6x^1. So if we again drop the power and decrement the power, we obtain 6x^0. Which is 6

3. Lastly, 2 which is actually 2x^0. So if we do the same again, we get 0x^-2. 0 multiplied by anything is 0. Therefore 2 differenciated with respect to x is 0.

Adding up add the differenciated terms results in 2x + 6 + 0. So dy/dx = 2x + 6.

Tarun S. GCSE Maths tutor, A Level Maths tutor, Mentoring HTML & CSS ...

9 months ago

Answered by Tarun, an A Level Maths tutor with MyTutor

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


£22 /hr

Ayyub A.

Degree: Mathematics Msci (Bachelors) - Bristol University

Subjects offered:Maths, Further Mathematics + 1 more

Further Mathematics

“Hi I'm Ayyub, current student at Bristol university studying Maths. I have significant tutoring experience in maths and hopefully i'll be able to help you out.”

£30 /hr

Michelangelo M.

Degree: MMath Mathematics with Placement (Masters) - Bath University

Subjects offered:Maths, Italian+ 4 more

Further Mathematics

“Mathematics student at the University of Bath, willing to help you love this subject and improve your grades.”

£20 /hr

Samuel J.

Degree: Physics (Masters) - Manchester University

Subjects offered:Maths, Physics


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

About the author

Tarun S.

Currently unavailable: until 30/11/2016

Degree: Computer Science (Bachelors) - Imperial College London University

Subjects offered:Maths


“I am very passionate about the study of mathematics and enjoy breaking down complex problems into simple solutions whilst explaining the process of doing so. I adapt my teaching methods to the each student to try and maximise their gr...”

MyTutor guarantee

You may also like...

Posts by Tarun

How can i solve the following simultaneous equations? 5x + y = 4 and 3x + 2y = 5?

How do i differentiate the equation y = x^2 + 6x + 2 with respect to x.

How do i factorise 20 + 10x?

How do i solve the quadratic x^2 + 5x + 6 = 0 ?

Other A Level Maths questions

What is dot product and how to calculate it?

The quadratic equation 2x^2 + 8x + 1 = 0 has roots x1 and x2. Write down the value of x1+x2 and x1*x2 and find the value of x1^2 + x2^2

How do I simply differentiate and what does a differential mean?

How do I integrate by parts?

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