Find the derivative of the given function. Use all lower case letters.

w(q) = 9a(b^8)q

The only reason I'm putting parenthesis in this problem is just to emphasize that q is not part of b^8. I'm not really sure how to do this just because there are so many letters.

Question

Find the derivative of the given function. Use all lower case letters.

w(q) = 9a(b^8)q

The only reason I'm putting parenthesis in this problem is just to emphasize that q is not part of b^8. I'm not really sure how to do this just because there are so many letters.

mathmale · Answer

First, I appreciate your using parentheses for clarity.  Good job!

w(q) = 9a(b^8)q

appears to be a function of q alone; I'd treat a and b as constants, at least initially.

mathmale · Answer

w(q) = 9a(b^8)q$$w(q) = 9a(b^8)q$$

Is this what you meant?  If not, please vix it.

mathmale · Answer

fix it, I meant.

anonymous · Answer

On Webstudy it looks like this:
$$w(q)=9ab^8q$$

The way it looks is what is confusing me. I can't tell if a and b are together or separate variables but just thrown together.

mathmale · Answer

Look at the label:   f(q).  To me, that indicates that f is a function of q alone, and that a and b are thus to be treated as constants.

What would be df/dq if you had f(q)=q?

anonymous · Answer

The answer would be 1 in that case, right?

mathmale · Answer

Yes.  What would be the derivative with respect to q of    p(q)=(a^3)q?

anonymous · Answer

Wouldn't that be 0? Since you are multiplying q by the derivative of a constant, which is 0.

mathmale · Answer

No.  Instead, you must treat (a^3) as the whole thing were a constant coefficient.  
Try again.   What is the derivative, with respect to q, of my sample function?

mathmale · Answer

If y=5a*q, dy/dq=5a*1=5a

anonymous · Answer

Ohhh... Alright. I think I get it.

mathmale · Answer

Happy for you.  Good luck!  Contact me again when you have more questions.