need help with the attachment

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need help with the attachment

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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1 Attachment
a) Just plug in 1 for the numerator and g(x) for the denominator in the quotient rule. b) \[ -{\frac {1+k{{\rm e}^{s}}}{ \left( s+k{{\rm e}^{s}} \right) ^{2}}} \] assuming y is a function of s. c) Follows from \[ x^{-n} = \frac{1}{x^n} \] and \[ \frac{d}{dx} x^n = nx^{n-1} \]
is the quotient rule the same thing as the reciprocal part b?

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Other answers:

What do you mean? The reciprocal rule is a special case of the quotient rule. You can use either one for part b, but it's easier to use the reciprocal rule.
The quotient rule f'g-fg'/g^(2)
but g(x) is just a variable
ok I got it
What is your question? g is not just a variable, it's a function.
Ok, hit good answer.
OK I need help with differentiating the bottom on part could you show me step by step how to differentiate that one?
part b
and also the numerator of the function
You need to differentiate\[ \Large s+k\cdot e^s \] with respect to s.
The derivative of a sum is the sum of derivatives, so differentiate s and then differentiate k*e^s.
What is the derivative of s?
1 Attachment
1
Yes. And what is the derivative of e^s ?
@ta, see the attachee
e^(s)
Your attachment doesn't include part b) explanation, thats what he asked about.
Yes, so now you can add them together and you get the derivative
And then just plug that into the formula in part a)
1+e^(s)
No! Don't forget the factor k!
k does not depend on s, so you can just leave it unchanged
But you must not forget it :D
1 Attachment
here u r
raheen there is still no explanation of part b :D
been answered all
part b asking to find using the rule only
ta123 do you have more questions?
whears the other 2 parts are to prove
@ta got that?
lol raheen are you just trying to get a medal, because I can give you one if thats what you want :D
your answer is wrong raheen, I got -1-ke^(s)/(s+ke^(s))^2
no YThe, I always try to help , pls don read the things in wrong way
Your answer is correct ta.
yes, thanks for the help Y and raheen
ta why some ppl are using an offensive words?
I think I stayed with u b4 more than 2 hrs, without any annyance, right?
yes
thank u.
no prob!

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