1 + x - 4*sqrt(x)
--------------------
x

(line is a division line)
Find the derivative of this function.

I don't know how halp.

This post was edited by desertwolf on Mar 6 2014 07:47pm

http://en.wikipedia.org/wiki/Quotient_rule

g(x) = 1 + x - 4*sqrt(x)
h(x) = x

the function f(x) = g(x)/h(x)

calculate g'(x)
calculate h'(x)

plug it into the formula
f'(x) = [g'(x)*h(x) - g(x) *h'(x)]/[h(x)]^2

You don't need the Quotient rule to solve this problem. You can break up the numerator into three fractions.

1/x + x/x -4sqrt(x)/x

d/dx(1/x) = -1/x^2
d/dx(x/x)=0
d/dx(-4sqrt(x)/x)=-1/2 *x^(3/2) or 1/2 * 1/cuberoot(2)


-1/x^2 + 2/x^3/2 simplifies to (2sqrt(x)-1)/x

My simplification:

find LCD: (-x^(3/2)+2x^2)/x^2x^(3/2)
simplify denominator, rearrange numberator: 2x^2-x^(3/2)/x^3. --- x^2 * x^(3/2) = x^3.
factor out x^(3/2).

(-1+2x^(1/2))/x^2

which becomes (2sqrt(x)-1)/x

Well technically you don't need the quotient rule to solve any problem, just bring the denominator into the numerator and use the chain rule. I never use the quotient rule. But its good to know for tests, when the instructor hits you with that evil "calculate the derivative using the quotient rule" question.

(a + b)/c = a/c + b/c

i see a LOT of calculus students who don't realize this - it comes in handy

True. Move the x to the top and make it x^(-1) and then use power rule; however, this early on in Calc I I'll bet anything he is being enforced to use the quotient rule with the problem as is.

Therefore,



You want to use this approach. Besides, it's great to practice the quotient rule because later on in calc I, II, III I'm pretty sure, if I can remember correctly, there are times when there is no way past the quotient rule.
Might as well get use to it now.