Calculus- Differentiating Help? (1 Viewer)

[Redyapper]

Hi,

When you differentiate (5x+3)^3, which then equals 3(5x+3)^2, how do you get to 15(5x+3)^2? Is it because you multiply it by the derivative of (5x+3), which is 5? But why do you do that? Because I thought you only did that if there was only 1 function of x...

Sorry, this is a really confusing question. Hopefully someone will be able to understand!

Thanks.

 

[RealiseNothing]

 

[Redyapper]

Oh ok it was what I thought... but I thought you only use Chain Rule when there's only one function of x, but in "(5x+3)^2", there are 2 functions of x because of the power of 2... Hard to explain, but maybe I was wrong.

 

[asianese]

5x+3 IS a function of x!! You are multiplying by 5 and adding 3! That is a function! Hence you must use the chain rule.

 

[Redyapper]

Ooohh I see. Thanks for the help everyone

 

[Peeik]

To answer your question quickly, yes. You must remember to multiply by the derivative of the 5x+3 to get the 15 in your answer.

Why you might ask?

It is because we need to use the chain rule for differentiating in order to differentiate y= (5x+3)^3. The reason we need to use the chain rule is because we have a function (namely, 5x+3) within another function (namely, the exponent: ^3). See the image below

 

[Redyapper]

Very helpful answer, thanks!

 

[RealiseNothing]

Oh ok it was what I thought... but I thought you only use Chain Rule when there's only one function of x, but in "(5x+3)^2", there are 2 functions of x because of the power of 2... Hard to explain, but maybe I was wrong.

The whole point of the chain rule is to differentiate functions with powers.

 

[nightweaver066]

The whole point of the chain rule is to differentiate functions with powers.

Functions of a function**