Find the derivative of the following expression: y=x^3+2x^2+6x+5.

  • Google+ icon
  • LinkedIn icon
  • 664 views

As the expression contains 4 separate terms that are added together, we can treat this as 4 separate differentiations. The general rule for differentiation for a general term bx^n is (b*n)x(n-1). For example, the first differentiation in this question is for x3, which would lead to (3*1)x(3-1), as b is just 1, which can be simplified to 3x2. Carrying on, we can find the following differentiations, which are:

2x2 goes to 4x

6x goes to 6

5 goes to 0

The final differentiation is 0 due to the fact that while it is written in the question as 5, we can actually think of it as 5x0. This is due to the fact that anything to the power of 0 is 1, leaving just 5. Using the general rule again, this would give the result of (5*0)x(0-1) = 0.

The final result is therefore dy/dx = 3x2+4x+6.

Matthew N. A Level Maths tutor, GCSE Maths tutor, A Level Chemistry t...

About the author

is an online A Level Maths tutor with MyTutor studying at Manchester University

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

95% of our customers rate us

Browse 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

mtw:mercury1:status:ok