Question

Differentiate f and find the domain of f if f(x)=x^2 ln(100−x^2)

Answer 1

2xln(100-x^2)-(2x^2/(100-x^2)) i found this as the derivative but im having trouble finding domain

Answer 2

we also have to enter the domain as an interval or union of disjoint intervals

Answer 3

to find the domain...you just need to know the domain restriction

for logarithms, the restriction is that the argument should be greater than 0

Answer 4

does that help?

Answer 5

yes a bit i just dont know how to format to domain using (numbers ) U (numbers)

Answer 6

also...seeing as you have a rational expression...your denominot also shouldn't be equal to 0

Answer 7

would you like to see what that format looks like?

Answer 8

yes please and i figured out that x cannot equal -10 and 10 right?

Answer 9

that only works for the domain of the rational function

Answer 10

remember i said...for logarithms...the argument should be GREATER than 0...so the domain is actually x > 10 and x> -10

Answer 11

anyway...here comes my example

Answer 12

\[\frac 1{x^2 - 4} + \ln (x^2 - 4)\]

i suppose you can see here that x cannot be equal to 2 and - 2 (from the rational function) and x should be greater than 2 and less than -2 (from the logarithm).

so i first write it as inequalities \[x \ne 2\; ; \;x \ne - 2 \; ; \; x > 2\; ; \;x < -2\]

if you notice... x> 2 and x < -2 also include x not equal to 2 and x equal to -2 in them...so you can write it simply as x > 2 and x< -2 without those not equal to

now to interval notation... x i s greater than 2 and less than - 2 means \[ (-\infty, -2) \cup (2, \infty)\]
this means that x can be any number as long as it's less than -2 and greater than 2

got it?

Answer 13

so my answer should be (-inf, -10)U(10,inf) ?

Answer 14

right

Answer 15

ok thank you !!

Answer 16

welcome

Answer 17

i was think about this again and i dont think that can be right... ln(100 - (-11)^2) wont work so it cant include numbers that are less than -10 ... so it cant be from negative infinity to -10 ??

Answer 18

ok i solved it kind of, so x can only exist between (-10, 10) is what i got

Answer 19

thank you for your help though!

Answer 20

ahh yes...i overlooked that..sorry