Question

Quick question. h(x)=[sqrt(2)*sec(x)]/3. I started this one w/ the quotient rule. The instructor started by placing the constant out front and totally ignoring it so that the constant was in the final answer. That doesn't seem right to me. If it is then I have a conceptual error.

Answer 1

Hmmm... I'm doing a couple of practice problems and they all work out the same - such that the derivative is not considered for the constant. i.e. f(x)=-sqrt(6)*sinx ==> f'(x)=-sqrt(6)*cosx. Can someone explain that? You don't have to take the derivative of the ENTIRE original function?

Answer 2

It is recommend to take out the constants when you do the derivative. you need to apply quotient when you have a function of x in the denominator.

Answer 3

It is recommended to take out a constant when you do the derivative and you need to apply quotient rule when there is a function of x in the denominator.

Answer 4

** I started this one w/ the quotient rule. ***
you would use this rule for a fraction with *variables* in the numerator and denominator

if you have f(x)/3 you can think of this as
c * f(x) (a constant c= 1/3 multiplying f(x) )
and we know
\[ \frac{d}{dx}\left( c f(x) \right)= c \frac{d}{dx}f(x) \]
i.e. we can factor out the constant.

Answer 5

Sorry, I bumped this but didn't realize it was already answered! I'm not used to this interface yet.

Answer 6

ok, thanks for confirming. the reason the quotient rule doesn't apply is because there is no "function" in the denominator (in this case). Correct?

Answer 7

yes... no function or variable that you are taking the derivative of in the denominator.

Answer 8

Thank you!