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lau22
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can someone help me simplify the derivative of x/sqrt(1x^2) ? This is for problem 5A3G of the second problem sets, and I think my proficiency with radicals may not be up to snuff to be able to properly solve this.
 one year ago
 one year ago
lau22 Group Title
can someone help me simplify the derivative of x/sqrt(1x^2) ? This is for problem 5A3G of the second problem sets, and I think my proficiency with radicals may not be up to snuff to be able to properly solve this.
 one year ago
 one year ago

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Topi Group TitleBest ResponseYou've already chosen the best response.1
What do you mean by simplifing? Let's calculate the derivative first:\[\frac{ d }{ dx }\frac{ x }{ \sqrt{1x ^{2}} }=\frac{ d }{ dx }x(1x ^{2})^{\frac{ 1 }{ 2 }}=x \frac{ d }{ dx }(1x ^{2})^{\frac{ 1 }{ 2 }}+(1x ^{2})^{\frac{ 1 }{ 2 }}\]\[=x(\frac{ 1 }{ 2 }(1x ^{2})^{\frac{ 3 }{ 2 }})\frac{ d }{dx }(1x ^{2})+(1x^2)^{\frac{ 1 }{ 2 }}\]\[=\frac{ 1 }{ 2 } x(1x^2)^{\frac{ 3 }{ 2 }}(2x)+(1x^2)^{\frac{ 1 }{ 2 }}=\frac{ x^2 }{ \sqrt{(1x^2)^3} }+\frac{ 1 }{ \sqrt{1x^2} }\]If you want to take that over common denominator, you have to multiply the last term with\[\frac{ 1x^2 }{ 1x^2}\]so you get\[\frac{ x^2+1x^2 }{ \sqrt{(1x^2)^3} } = \frac{ 1 }{ \sqrt{(1x^2)^3} }\]That might be the simplest form for that derivative.
 one year ago

lau22 Group TitleBest ResponseYou've already chosen the best response.0
thank you very much! that's exactly what I needed!
 one year ago

herradajeoffre18 Group TitleBest ResponseYou've already chosen the best response.0
thank you
 one year ago
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