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Study23
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Hmm.. I'm having difficulties differentiating this function: \(\ \frac{x}{x+\frac{c}{x}} \). Help, please!
 one year ago
 one year ago
Study23 Group Title
Hmm.. I'm having difficulties differentiating this function: \(\ \frac{x}{x+\frac{c}{x}} \). Help, please!
 one year ago
 one year ago

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Mathmuse Group TitleBest ResponseYou've already chosen the best response.2
function of x. c and z are constants. Direct quotient rule
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
@Mathmuse The fraction is \(\ \Huge \frac{c}{x}.\)
 one year ago

Mathmuse Group TitleBest ResponseYou've already chosen the best response.2
my bad, could not see it properly. In that case, get a common denominator of x on the bottom.
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
Could you help me with that?
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
Could I substitute the fraction with \(\ \huge c^{x} ? \)
 one year ago

Mathmuse Group TitleBest ResponseYou've already chosen the best response.2
\[\frac{x}{x + \frac{c}{x}}=\frac{x}{(\frac{x^2+c}{x})}=\frac{x}{1}\frac{x}{(x^2+c)}\]
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
So how I go use the quotient rule to differentiate this function?
 one year ago

Mathmuse Group TitleBest ResponseYou've already chosen the best response.2
right. Or, because i always mess up the quotient rule, convert it to product rule
 one year ago

Mathmuse Group TitleBest ResponseYou've already chosen the best response.2
\[\frac{x}{x^2+c}=x*(x^2+c)^{1}\]
 one year ago

Mathmuse Group TitleBest ResponseYou've already chosen the best response.2
both will work
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
\[(\frac{ x^2 }{ x^2+c })'=\frac{ (x^2)'(x^2+c)(x^2+c)'x^2 }{ (x^2+c)^2 }\]
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ 2x(x^2+c)2x(x^2) }{ (x^2+c)^2 }=\frac{ 2xc }{ (x^2+c)^2 }\]
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
Where did \(\ \Huge x^2+c \) come from??
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
@Mathmuse didnot write x^2 as nominator
 one year ago

Mathmuse Group TitleBest ResponseYou've already chosen the best response.2
for shame
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
\[x+\frac{ c }{ x }=\frac{ x^2+c }{ x }\]
 one year ago

Study23 Group TitleBest ResponseYou've already chosen the best response.0
So how does that become x^2+c?
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
\[x \div \frac{ x^2+c }{ x }=x \times \frac{ x }{ x^2+c }=\frac{ x^2 }{ x^2+c }\]
 one year ago

Jonask Group TitleBest ResponseYou've already chosen the best response.0
so we derived this
 one year ago
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