Question

How to differentiate?
x^2/x-11
Quotient rule?

Answer 1

u dont like quotient rule, do u

Answer 2

lol :)

Answer 3

he likes converting it to neg exponents and working product rule i think :)

Answer 4

^ Indeed

Answer 5

Product Rule is easier to remember, that's for sure.
Don't have to worry about getting the subtraction backwards.

Quotient Rule can save you some trouble with simplifying though :o

Answer 6

Okay quickly answer this question and then get back to the first question:
f(u)=u^2
g(x)=u=x^5+2
Find (f o g)'(-1)
Would it just be f'(-1)=(x^5+2)^2

Answer 7

\[\Large \left(\frac{x^2}{x-11}\right)'\quad=\quad \frac{\color{royalblue}{(x^2)'}(x-11)-x^2\color{royalblue}{(x-11)'}}{(x-11)^2}\]

Answer 8

That's for the first question. Oh composition stuff? :hmm

Answer 9

g(x)=u ???
Hmm so I guess we're taking our derivative with respect to uhhhhhhh...... x i think.\[\Large f(\color{teal}{g(x)})\quad=\quad f(\color{teal}{u}) \quad=\quad u^2 \quad=\quad (x^5+2)^2\]Mmmm I dunno, this one is so weird... D:

Answer 10

@hartnn

Answer 11

\[\Large \frac{d}{dx}f(g(x))\quad=\quad 2(x^5+2)(5x^4)\]
Mmmmmm like that maybe? +_+

Answer 12

Evaluated at x=-1,\[\Large 2\left[(-1)^5+2\right]\left[5(-1)^4\right]\]

Answer 13

Somethinggggggg like that? :o