Question

Differentiate the function with respect to x:
y=((x+5)^5-1)^1

Answer 1

\[y=((x+5)^{5}-1)^{4}\]

Answer 2

chain rule ?? :)

Answer 3

\[4((x+5)^{5}-1)\]

Answer 4

do I use the power rule next?

Answer 5

wait it should be \[4(((x+5)^{5})-1)^{3}\]

Answer 6

i think...

Answer 7

Are you sure that your expression ends in ^1?

Any base, other than 0, raised to the power 1, is equal to the base itself.

Check to ensure you have copied the problem correctly.

Answer 8

What about if you divide it into pieces?

Answer 9

i originally wrote it wrong @mathmale

Answer 10

yes ^^ that's correct
starts with the power rule \[\huge\rm y= x^n \rightarrow y=nx^{n-1}\]
and since it's a composition function you have to take the derivative of the inner function
\[y=(\color{ReD}{(x+5)^5 -1})^4\]
\[y=(\color{ReD}{(\color{blue}{x+5})^5 -1})^4\]

Answer 11

\[y=u^4\]
and
\[u=g^5-1\]
and
\[g=x+5\]

I think it would be simple for you rather than differentiating it as one shot!

Answer 12

so -1 will become 0?

Answer 13

yes the derivative of constant is 0

Answer 14

\[\frac{ dy }{ dx }=\frac{ dy }{ du }*\frac{ du }{ dg }*\frac{ dg }{ dx }\]
chain rule as all know

Answer 15

so it would be \[y=20(x+5)^{4}(5)\]

Answer 16

100(x+5)^4 ??

Answer 17

wait im off

Answer 18

really off

Answer 19

it'' just be 20(x+5)^4 or no?

Answer 20

Looking at your specific problem:\[4(((x+5)^{5})-1)^{3}\] Do the following in order:
1. apply power rule to \[4(((x+5)^{5})-1)^{3}\]

Show your work, please. Then we'll discuss the next step.

Answer 21

3mar: Your question is a good one, but is totally irrelevant to juan's question. Wait.

Answer 22

oh i see I keep forgetting to subctract 1 from the exponent

Answer 23

Apply the power rule to the given expression, please. Want to see YOUR work.

Answer 24

ok let me just try to do it on paper, I was doing it in my head lol

Answer 25

you should keep the derivative of the outer function
lets start with the easy one \[y=(\color{Red}{x^2+3})^3\]

\[\rm y'=3(\color{Red}{x^2+3})^2 \cdot D~of~(\color{Red}{x^2+3})\]
\[y'=3(\color{Red}{x^2+3})^2 \cdot \color{Red}{2x}\]

Answer 26

I just noticed multiple errors of mine now, lol

Answer 27

it's impossible to do these type of questions without paper/pencil

Answer 28

yeah I learned the hard way

Answer 29

would you please do the entire problem, or as much of it as possible, and then share your end results. Please skip the asides (e. g., yeah, I learned the hard way).

Answer 30

smh, someone closed my question and they expect me to learn

Answer 31

This medal for the colour, Nnesha!
Thank you.

Answer 32

There can someone just give me the answer at least, so that I can find my way through

Answer 33

I give up on this website, its too time consuming anyways laters #Nochill @mathmale

Answer 34

Sorry you're fed up. However, you must be honest with yourself: Did you actually use any of the suggestions I gave you? Did your several irrelevant remarks help you solve this problem or help anyone else to guide you?

I challenge you to post a simpler function requiring application of the power and chain rules and work through this problem, and then to attempt again the one at hand.

Answer 35

Truthfully I was doing your "suggestions", you don't understand since you are smart, and on my previous questions I didn't understand a word you said. How about you listen to one of my suggestions, put yourself in the shoes of another and please be more comprehensive, after all we are all human

Answer 36

For the HUMBLE shall be Great, and the Great shall be Humbled