**Examples on differentiation using product rule or sum rule**

**DIFFERENTIATION IS VERY EASYâ€¦..I want you to repeat that mantra three times, for those that have develop this mindset of, CALCULUS IS HARD**

**Now let’s look at simple differentiation..,â€¦..like for example**

y=2xÂ² +x +1. Find dy/dx

**The power of the first x is 2, so the coefficient of the same first x is 2**

**For the second x**

**The power is 1 and the coefficient is still 1**

**And the last, has just 1( and invisible x^0)****So after identifying this knowledgeâ€¦â€¦you can proceed to the next step**

**Differentiation**

**dy/dx = (power of x) multiply by (the coefficient of x) and remove 1 from the power of x**

**A practical example,**### y=2xÂ² +x +1. Find dy/dx

**dy/dx = 2Ã—2â€¢X^(2-1) + 1Ã—1â€¢ X^(1-1) + 0Ã—1â€¢ X^(0-1)**

**dy/dx= 4â€¢X^(1) + 1â€¢ X^(0) + 0â€¢ X^(-1)**

**dy/dx= 4X^1 + 1 + 0**

**dy/dx= 4X+ 1 ( final answer)**

**Note: anything raise to power zero (0) is One (1)**

**And zero(0) multiply by anything is zero (0)**

**Please look at this any question please****Before I proceed,**

**Okay for beginners only, try this and inbox me your answers on the comment box below.â€¦ I’ll reveal the winner**

### PRODUCT RULE

Okay next topic is on product rule, we just finished what we know as sum rule

Product rule is very simple easy and interesting say that five times, so it can stick (with God all things are possible)

**What’s product rule? Prod****uct simply means the multiple of two or more things.**

**For example 3x^2 [4x + 1]**

**How do you differentiate? But you’ll observe that the both of them are connecting with product rule**

**For instance, (3x^2 [4x + 1]) = 3x^2 â€¢ [4x + 1])**

**I.e 3x^2 Ã— [4x + 1])**

**So whenever you observe anything like that, you make use of product rule,**

**For example, let’s differentiate**

Â

**y = 3x^2 [4x + 1]**

**Solution****y = 3x^2 [4x + 1]****We can’t differentiate this directly, then we’ll apply product rule.**

**Product rule, dy/dx = Udv + vdu**

**Â ****What’s U and what’s V?**

**In . y = 3x^2 [4x + 1]****Let u = 3x^2****And V = 4x + 1**

**Now differentiate U and V (using sum rule)**

**Let u = 3x^2****du/dx = 6x**

**And V = 4x + 1****dv/dx = 4**

**Recall from product rule****dy/dx = Udv/dx + vdu/dx**

**So substitute the value for u, dv/dx, v and du/dx there**

**Product rule, dy/dx = Udv + vdu**

**dy/dx = 3x^2 Ã— 4 + 4x + 1 Ã— 6x****dy/dx = 3x^2 â€¢ 4 + 4x + 1 â€¢ 6x****dy/dx = [3Ã—4 x^2 ]+[ 4x Ã— 6x + 1 Ã— 6x]**

**dy/dx = [12x^2 ]+[ 24x^2 + 6x]****=12x^2 +24x^2 + 6x****=36x^2 + 6x ( final answer)**

**Note: alike terms can add themselves but unlike terms can’t. For instance,**Â t**he coefficient of x^2, can be added to any coefficient of x^2 ( i.e tomato can add tomato but pepperÂ can’t add with Tomato)**

Say this mantra, product rule is very easy five times, then study this again.Â

**Related content**

**Do you know limit very well, if not check this now (limit@infinity)**

**Find the limits of 7-3x^2+6x^5/ 2+x-3x^5 as x approaches infinity**

**In other words, find the limits of 7- 3x square + 6x raise to power 5/ 2 + x – 3x raise to power 5**

**Watch video**Â on differentiationÂ

Â

Â

Thanks for the good writeup. It if truth be told was once a amusement account it.

Glance complex to more added agreeable from you! By the way,

how could we keep in touch?

This is a topic that’s near to my heart… Thank you!

Where are your contact details though?

you are actually a just right webmaster. The web site

loading pace is incredible. It sort of feels that you are doing

any unique trick. Moreover, The contents are masterpiece.

you’ve performed a fantastic activity in this subject!

Normally I do not learn article on blogs, but I would like to say

that this write-up very forced me to take a look at and do so!

Your writing style has been amazed me. Thank you, very great article.

Howdy very cool website!! Guy .. Beautiful .. Superb

.. I’ll bookmark your blog and take the feeds also? I’m glad to

seek out so many useful information right here in the publish, we want work out

extra techniques on this regard, thank you for sharing.

. . . . .

You’re welcome

I’m more than happy to find this site. I wanted

to thank you for your time for this fantastic read!! I definitely enjoyed every part of it

and I have you bookmarked to check out new stuff in your site.

Okay buddy, I appreciate your feedback

Nice response in return of this difficulty with

firm arguments and explaining everything about that.

More loves

I have to thank you for the efforts you have put in writing this site.

I’m hoping to see the same high-grade blog posts from you later on as well.

In fact, your creative writing abilities has motivated me