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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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