Product Rule for Derivatives (Calculus)

The product rule is one of the fundamental derivative rules in calculus. It shows you how to take the derivative of the product of two functions: f·g. In this video we will introduce the product rule, talk about common mistakes, and give several examples.

What to watch next:

The Tangent Line & the Derivative

Quotient Rule

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Written and Produced by Michael Harrison

Michael Harrison received his BS in math from Caltech, and his MS from the University of Washington where he studied algebraic number theory. After teaching math for a few years, Michael worked in finance both as a developer and a quantitative analyst (quant). He then worked at Google as a software engineer for over 5 years before leaving to found Socratica.

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[glennrickelton]

I only studied your first example in your video and I have to say: "Thank you!" Your lesson does not just carry out the Product Rule in operation but shows why it works and proves it gives the same answer if the two equations were multiplied by each other and the derivative then taken. The Product Rule now makes sense

[manoharanpgt]

Sir,
We the people of the world will grow through you, The abstract becomes Thank sir.

[ephrataguracha]

this is probably the best calc video i've ever seen, thank you

[christianhardy]

Socratica's videos are highly intuitive, which makes them so amazing! Do you plan on covering the chain rule in the future?

[alopexcheung]

I have watched a lot of calculus video before but no one better than yours. Thanks your great jobs. :D

[gaupau]

I just finished grade 11 and math isnt my strongest point, but i love chem and bio and i really enjoy learning about it! And im watching these videos to prepare me for calculus. Thanks!

[alexandrupostole]

Great video! Keep it up! Im a chemistry student that only begins with the basics of maths and i really appreciate your videos! :=)

[majdihassan]

thanks for your explanation.it is important that you explain by proving the formula.

[infinitymfg]

This was a really easy method to follow, it will be easy for students to understand it.

[jerrygundecker]

When this video was over, I had to go back to the video about how to handle stress. It helped.

[zubairhaleem]

A very good presentation of basic calculus rules. please explain the derivatives by using 'ab-nitio' method, and power rule for calculating derivatives quickly.
Great work please keep it up..

[moamensmathsplatform-mmp]

I hope you all the best and I hope you good health . what is the derivative of y with respect to x for y= (x3+2x2+x)^3 ?
I suggest these steps to find dy by dx

1. bring down the power in the front of the bracket as a multiplier.
or bring down the power to the front of the bracket as a multiplier. it is better to put the preposition (in) or (to) in the above sentence .
2. reduce the power by one
3. multiply the derivative of the inside function.

dy/dx = 3 (x3+2x2+x)^2 (3x2+4x+1)

Would you please recommend and advise me what are the best method to find dy by dx ?

All the best

Moamen Saeed Talha

[escupetube]

Awesome! Calculus is very interesting :)

[jacobkhu-oldacc.]

are there any upcoming videos on calculus? I couldn't seem to find any. great vid though

[felipecas]

Great video and explanation. How do you animate the typewrite effect with the mathematical text?

[yaraahmed]

Thank you so much it definitely helped me!😊😊😊

[bohnec]

Well, you could simplify it at the end with the following: 17*(e^x)*(cosx - x*sinx + x*cosx) but whatever. Anyways, a nice video, I liked it

[ejecutor]

your videos are so interesting but somewhat advance reducing dramatically the audience that can understand and take advantage of the knowledge given by video

[eurosenelsuelo]

It's nice to learn how to do it but I was expecting to see why does it work. I mean the demonstration explained. But don't get me wrong, I think it's a great and very useful video

[MRSDR]

Can the last equation at 10:57 also be written as 17e^x(cosx - xsinx + xcosx)? Not that's much nicer though.