Question

need help on the attachment

Answer 1

What about it is confusing you? I presume you're having difficulty understanding the chain rule?

Answer 2

for my answer I got 1+x/(x^(2)+25) which is not one of the answer choices

Answer 3

no I'm not having trouble with the chain rule it just my answer is not right which I'm sure why

Answer 4

first, break it up into two problems and attack it seperately

arctan is 1/1+x^2 so that one is

1/(1+(x/5)^2)(1/5)

then do the ln

ln(x) is 1/x

so that one is 2x/sqrt(25+ x^2)

put them together

1/5 1/(1+ (x/5)^2) + 2x/sqrt(25+x^2)

is that one of the answers?

Answer 5

here are the answer choices

Answer 6

I forgot the first answer choice which too.

Answer 7

its #4, I must have reduced wrong...I think my reslult should have been 1/2 not 2

Answer 8

I still don't see how you get number 4, aren't you suppose to use stand-form for arctan

Answer 9

http://www.wolframalpha.com/input/?i=differentiate+artctan%28x%2F5%29+%2B+ln%28sqrt%2825%2Bx%5E2%29%29


click on show steps...

Answer 10

Their steps are way to complex.

Answer 11

Okay, let's walk you through this...

Answer 12

Thanks!

Answer 13

You are told that\[f(x)=\tan^{-1}(\frac{x}{5})+\ln\sqrt{25+x^2},\]and are asked to differentiate that function. Well, notice that this can be re-written as follows:\[\frac{df}{dx}=\frac{d}{dx}[\tan^{-1}(\frac{x}{5})]+\frac{d}{dx}[\ln\sqrt{25+x^2}].\]From the definition of the derivative of inverse tangent and logarithm, we obtain the following:\[\frac{df}{dx}=\frac{1}{1+(\frac{x}{5})^2}\frac{d}{dx}[\frac{x}{5}]+\frac{1}{\sqrt{25+x^2}}\frac{d}{dx}[25+x^2].\]Deriving the remaining, simple expressions, we obtain the following:\[\frac{df}{dx}=\frac{1}{1+(\frac{x}{5})^2}\frac{1}{5}+\frac{1}{\sqrt{25+x^2}}2x.\]Now simplify all of that, and you'll have your answer.

Answer 14

My mistake; I forgot to perform the chain rule over the radical. The fourth expression above should be:\[\frac{dy}{dx}=\frac{1}{1+(\frac{x}{5})^2}\frac{1}{5}+\frac{1}{\sqrt{25+x^2}}\frac{1}{2\sqrt{25+x^2}}2x.\]

Answer 15

why is there a plus after 1/5?

Answer 16

Because the differential of a sum is a sum of differentials.

Answer 17

I not sure where getting the 1/5 from?? I'm using the standard form of arctan

Answer 18

oops! I meant to put where you getting the 1/5 from? which if you answer is the chain rule I know how to use it which is taking the derivative of the outside then inside, but I'm not using it here.