document.write( "Question 969163: How do I differentiate y=sin^3x? \n" ); document.write( "
Algebra.Com's Answer #592105 by MathLover1(20850)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "If \"y=+sin%5E3%28x%29\"\r
\n" ); document.write( "\n" ); document.write( "it is same as\r
\n" ); document.write( "\n" ); document.write( "\"y=+%28sinx%29%5E3\"\r
\n" ); document.write( "\n" ); document.write( "let \"sin%28x%29=+u\", then \"du%2Fdx+=cos%28x%29\"\r
\n" ); document.write( "\n" ); document.write( "and \"y=+u%5E3\", then \"dy%2Fdu=3u%5E2\"\r
\n" ); document.write( "\n" ); document.write( "using chain rule\r
\n" ); document.write( "\n" ); document.write( "\"dy%2Fdx=%28dy%2Fdu%29+%2A%28du%2Fdx%29\"\r
\n" ); document.write( "\n" ); document.write( "=>\"+dy%2Fdx=+3u%5E2+%2A+cosx\"\r
\n" ); document.write( "\n" ); document.write( "recall that \"u=+sin%28x%29\"\r
\n" ); document.write( "\n" ); document.write( "=>\"+dy%2Fdx=+3%28sin%28x%29%29%5E2+%2A+cos%28x%29\"\r
\n" ); document.write( "\n" ); document.write( "=>\"dy%2Fdx=+3sin%5E2%28x%29cos%28x%29\"\r
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