chain rule derivative

[Dorian Gray]

Good Day Mathematicians,

I was wondering if somebody could please tell me why a^3 in this problem is 0? Why is it not treated like any other variable such as x? Thanks for your input, suggestions, comments, advice. A short, sweet, and simple would be much appreciated.
Thank you




I used this website. Some other people with questions may find it useful.

http://www.wolframalpha.com/input/?i=derivative+of+cos(a^3%2Bx^3)

I APOLOGIZE IF YOU CANNOT READ THE SCREENSHOT. I CANNOT MAKE IT LARGER FOR SOME REASON.

 

[Dorian Gray]

 

[pka]

The derivative of any constant is zero.
\(\displaystyle a^3\) is constant.

 

[Dorian Gray]

thank you

Thank you pka for your response. I am surprised that the author did not use "c" instead of "a".

 

[pka]

Thank you pka for your response. I am surprised that the author did not use "c" instead of "a".

In the notation \(\displaystyle \dfrac{d}{dx}\) the \(\displaystyle dx\) tells us that \(\displaystyle x\) is the variable(changing) and all else are treated as constants.

 

[Dorian Gray]

thank you

Thank you Pka and JeffM once again for your explanations one variable "a". My professor did not directly mention that x is the only variable hence seen in the leibniz notation by Pka (maybe since this is only the first day that we spent entirely on chain rule).

@JeffM I had never heard that before about the letters of the alphabet. I will definitely keep that in mind.