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 2 years ago
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.
 2 years ago
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.

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Topi
 one year ago
Best ResponseYou've already chosen the best response.1What 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.

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