Question about the quotient rule?

Question

When you use the quotient rule to find the derivative of a function, does the denominator of the function have to have a variable or can it be a constant number?

Answer 1

The function can be a constant. The quotient rule doesn't care what type of function you put in the denominator, so long as it is differentiable. Of course, as the previous posters have mentioned, the quotient rule is not required, but it is instructive to observe what would happen if you used it anyway. Consider the following derivative:

d(f(x)/c)/dx

Where f is a differentiable function, and c is a constant. Then using the quotient rule, this is:

(f'(x)*c - dc/dx * f(x))/c²

Of course, since c is a constant, dc/dx = 0, so we have:

(f'(x)*c)/c²
f'(x)/c

Which is exactly what you would get if you used the linearity of differentiation instead. So using the quotient rule isn't wrong, it is merely unnecessary.

Answer 2

The constants given in the function are always taken out of the derivative sign. whether in the numerator or in denominator. When denominator is a constant then it is taken out and we differentiate it. and if the denominator is a variable then we use the quotient rule. let me explain it by taking an ex.
if y = (x^2+3x)/5 then dy/dx = 1/5(2x + 3). here we have taken the constant 1/5 out of the sign of derivative.
and if y = (x+3)/(x+4) then we use the quotient rule.

Answer 3

it doesnt matter if the denominator was a constant or not. but if the denominator was a constant, you can find the derivative through easier means (without the quotient rule)

example:

f(x) = (2x +5) / 7 (7 being the constant denominator)
f(x) = (1/7) (2x+5)

Answer 4

Quotient rule is used if there is a variable on the denominator.

Answer 5

if the denominator is a constant, you can pull it out as a fraction and then you don't even have to use the quotient rule.

Answer 6

It can probably be a constant, but why waste your time -- you could rewrite the expression as a non-quotient.

For example (x + 1) / 2 could be rewritten as 0.5 * (x + 1)

Answer 7

it can be a constant I believe. g(x)*f'(x)-g'(x)*f(x)/g(x)^2


yea, you wouldn't need the quotient rule.