document.write( "Question 891484: If y = tan^-1(x/a)
\n" ); document.write( "So y'=a/(x^2+a^2) [by differentiating]
\n" ); document.write( " Y'=a/(x-ia)(x+ia) why does it become like this and where does the i comes from?
\n" ); document.write( "Sir, this question is from calculus (examples of finding nth derivative so please help me.) \n" ); document.write( "
Algebra.Com's Answer #539769 by Fombitz(32388)\"\" \"About 
You can put this solution on YOUR website!
When you look at the difference of two squares,
\n" ); document.write( "\"x%5E2-a%5E2=%28x%2Ba%29%28x-a%29\"
\n" ); document.write( "since,
\n" ); document.write( "\"%28x%2Ba%29%28x-a%29=x2-ax%2Bax-a%5E2\" so the x terms cancel out.
\n" ); document.write( "However when you look at the sum of two squares,
\n" ); document.write( "\"x%5E2%2Ba%5E2\" you have the same situation with trying to cancel out the \"x\" terms, however if you look at \"%28x%2Ba%29%28x%2Ba%29\" you get,
\n" ); document.write( "\"%28x%2Ba%29%28x%2Ba%29=x%5E2%2B2ax%2Ba%5E2\"} so that won't work.
\n" ); document.write( "You need the opposite signs to cancel out the x terms and you need the \"a%5E2\" term to have a negative coefficient.
\n" ); document.write( "Since \"i%5E2=-1\" then you can use \"i\" as the coefficient.
\n" ); document.write( "\"%28x-ai%29%28x%2Bai%29=x%5E2%2Baix-aix%2B%28ai%29%5E2\"
\n" ); document.write( "\"%28x-ai%29%28x%2Bai%29=x%5E2-a%5E2\"
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