When do you use Qoutien rule and when do you use product rule? Can I se either one? what's the difference?

Answer 1

I assume that you are talking about differentiation. The product rule tells you how to differentiate a function which is made up of two (or more) simpler ones multiplied together. The quotient rule applies to two functions, one of which is divided by the other. You can use the product rule instead of the quotient rule by writing u/v = u*v^(-1) but then of course v^(-1) has to be done as a function of a function (chain rule). I can't think of any situation when you would want to do the reverse as the product rule is the easier one to use.

Answer 2

the answer to your question is , Yes you can use either one.

the quotient rule is the product rule.

h(x) = f(x)g(x)

product rule gives: h'(x) = f'(x)g(x) + f(x)g'(x)

suppose that h(x) = f(x)/g(x) = f(x)1/g(x)

product rule gives:

h'(x) = f'(x)1/g(x) - f(x)g'(x)/g(x)^2
and simplifies as:
h'(x) = [ f'(x)g(x) - f(x)g'(x)]/g(x)^2

which we call the quotient rule.

You can use either one, you just need to tke the derivatives correctly. It really depends on the algebraic steps you'd rather perform. In the end the goal is to take the derivative of the product of two (or more) functions.

Answer 3

Quotient is used when there is a numerator and denominator
eg f (x) = 3x / (x² + 5)

Product is when multiplied together
eg f(x) =(x - 5) (x² +1)

Use as applicable.

Answer 4

If I am not wrong you are talking about differentiation.

quotient rule is used when there are two functions -one in numerator and another in denominator.

when two functions are in multiplication,product rule is used

Answer 5

I think you are referring to differentiation
we use product rule for differentiating a product of two terms
that is d(uv)=udv +vdu
for eg.
d(xsin(x))=x*d(sinx) +sin(x)*d(x)
=x*cosx +sinx (assuming the differentiation to be with respect to x)

quotient rule is used for the types d(u/v)
d(u/v)= (vdu-udv)/v^2
for eg.
d(sinx/x)= [x*d(sinx)-sinx*d(x)]/x^2
=[xcosx -sinx]/x^2
(again assuming the differentiation to be with respect to x)