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