Question

if g(x) = 2 tan(7x)
what is g'(x)=

Answer 1

Really, hicks, this is not a place to be asking for answers. We help, we don't do homework.

Answer 2

thing is, i'm not doing this for a grade... i just don't understand how to begin these problems

Answer 3

(d/dx)f(g(x))=g'(x)f'(g(x)

Answer 4

this is the chain rule you need to take the derivative of the outside multiplied by the derivative of the inside. so first you need the derivative of tan(x)

Answer 5

the formula makes sense now, but i still don't know how to go about approaching all the different circumstances

Answer 6

like a sqrt, or exponent or log

Answer 7

i definately need some algebra review. i haven't taken a single math class in 8 years and my school is forcing me to take calculus without allowing me to take the pre-requisites. and i'm trying to graduate this year, so no options but desperately trying to pass and i'm WAAY in over my head

Answer 8

and none of my teachers or TAs speak english, so when i go to tutoring, we don't understand eachother

Answer 9

you just have to practice and you can see it. you will have either simple constants to powers, products(two functions multiplied or a function in a function. so first is to identify what is the form of the equation such as sin(2x) is a function in the sin function

Answer 10

there are other possibilities of functions other than powers, products or chains, but these are the most common

Answer 11

hicksonm, if you really want to learn, go to KhanAcademy. It's a deliberately paced learning environment that can fill in gaps of knowledge very well.

Answer 12

i've been practicing for hours, but i have to look up EVERY step EVERY time i get to it. i don't remember how to do anything... i don't remember how to simplify things

Answer 13

how much does it cost?

Answer 14

Davidjohn, thanks for the explaination. that makes more sense than the variable soup in my book

Answer 15

oh my gosh, KhanAcademy is free! i'm watching one of their algebra videos now!

Answer 16

thank you thank you! finally, something that doesn't cost $300!

Answer 17

Yes, KhanAcademy is one of the best. ;D

But, really, the "variable soup" might be unintuitive, but it started out as such for all people. You just need to practice, practice, practice.

Answer 18

listen, i know people that come on here to mooch off y'all's goodwill

Answer 19

Answer: f(x) = 1 and g(x) = xx
BUT Answer:


no, f(x) = 1 and g(x) = xx are not the same function. The first function maps all values of x to 1. In essence, no matter what x is, the value f(x) will always equal 1. g(x) maps all values of x to the square of the number entered. For example, g(2) = 4 while f(2) = 1. Because the two functions do not have equivalent outputs for the same input, they cannot be the same function

Answer 20

reading math books is an art. they take practice and even then. so you have a 2tan(7x). or 2(f(g(x)) = 2 f '(g(x)) (g'(x)). so do you know what the derivative of tan(x) is? that will give you the f'(g(x)) where g(x) is the 7x function inside of the tangent.

After you find that you will need the derivative of 7x which will be your g'(x)

combine those to get 2(tan(7x))' (7x)'

Answer 21

SO DID THAT HELP???

Answer 22

but i promise i'm not that girl. i'm genuinely confused and pretty screwed... i really appreiate all of you

Answer 23

@hicksonm, I probably only speak for myself when I say this, but I don't come here to help people in the traditional sense. When someone asks a question, I answer it, not because I'm interested in them understanding it, but because I'm reinforcing MY understanding of it.

So, when you post a question, it would be lovely for others like me if you asked about an understanding issue instead of just copy-pasting homework.

Answer 24

i come on here sometimes to help but yeah i do it alot for my own practice and (here's the nerd part) its fun haha

Answer 25

makes sense. i'm still too rusty to ask an intelligent question, but i will give it my best shot

Answer 26

There's no such thing as an "intelligent" question. There's only what you know, what you don't know, and the questions you have to ask to bridge the gap.

Answer 27

mostly, just seeing you all run through the steps with the problems has helped me to put some of the puzzle pieces together

Answer 28

but back to your problem.
(tan(x))' = sec^2(x)
(7x)' = 7
so
2(sec^2(7x))(7) = 14sec^2(7x)

Answer 29

yes...

Answer 30

just giving the answer to check your work with

Answer 31

thanks! i was answering yes to the "back to your problem" comment

Answer 32

so, when there is a constant separated out, you save it until the end?

Answer 33

like the 2?

Answer 34

you don't take the deravitive of the 2?

Answer 35

Answer:


no, f(x) = 1 and g(x) = xx are not the same function. The first function maps all values of x to 1. In essence, no matter what x is, the value f(x) will always equal 1. g(x) maps all values of x to the square of the number entered. For example, g(2) = 4 while f(2) = 1. Because the two functions do not have equivalent outputs for the same input, they cannot be the same function
SO IT IS........... f(x) = 1 and g(x) = xx

Answer 36

so, it's not defined?

g'(x) doesn't =14sec^2(7x)?

Answer 37

let me check my work :/

Answer 38

i thought g was related to f in such a way that they weren't supposed to be equivalent? did i miss somehting big?

Answer 39

first off, you can always take the multiple in front of the derivative. a simple example.
(7x)' = 7
if you take the 7 out and just do x, its 1*7 = 7
a little bigger problem=

3x^2. take the 3 out so take derivative of x^2 = 2x taking the 3 back in is 3*2x

Answer 40

I'm not sure how relevant this is for me to inject, but if you're finding math counterintuitive, and you can't get around that, it's probably because you see math like a jigsaw puzzle or Rubik's cube.

Math is a language, a very *concise* and *logical* language. It's not a puzzle. Math is used to state and express puzzles and problems in a logical way, but math itself is a language. Never forget that.

Answer 41

what about the other person who said the functions were not equivalent?