Question

Find the derivative:
x=1, f(1)=2, f'(1)=-1, g(1)=-2, g'(1)=3. Find h'(1):
h(x)= xf(x)
------
x+g(x)

Answer 1

Probably need to use the quotient rule, so do that first to find h'(x).

Answer 2

After using the quotient rule (too hard to tell if it's done right, w/o equation editor)

plug in these x=1, f(1)=2, f'(1)=-1, g(1)=-2, g'(1)=3. Find h'(1)

Answer 3

I don't think you did that correctly... but as agent said, it's pretty hard to read :d\[\Large\bf\sf h(x)\quad=\quad \frac{x f(x)}{x+g(x)}\]

Answer 4

We start with quotient rule:
\[\Large\bf\sf h'(x)\quad=\quad \frac{\color{royalblue}{\left[x f(x)\right]'}[x+g(x)]- x f(x)\color{royalblue}{\left[x+g(x)\right]'}}{[x+g(x)]^2}\]

Answer 5

`Within` quotient rule, we will have product rule being applied to the first blue term.
Understand what's going on?

Answer 6

^you know none of that is showing up @zepdrix at least not for me.

Answer 7

ugh really ? :( it was working earlier.. grr

Answer 8

drawing tool is messed up also :c

Answer 9

Nothing even happens for me, when i click the equation or draw button.

Answer 10

h' = [ (xf' +f)(x+g) - x*f(1+g') ] / (x+g)^2

h' = [(-1+2)(-1) - 2(4)] / (-1)^2

h' = (-1 -8)/1

h' = -9

Answer 11

@dumbcow Thank you so much!

Answer 12

I tried it a different way, by changing f(x) and g(x) to variables, then changing them back, which also worked.