document.write( "Question 1003759: differentiate the following function:\r
\n" ); document.write( "\n" ); document.write( " (a)f(x)=(x^2+1/x^3 )(x^3-x^2+1)
\n" ); document.write( " (b)f(x)= e^((x^3+2x))
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #620445 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "(a)  \"f%28x%29=%28x%5E2%2B1%2Fx%5E3+%29%28x%5E3-x%5E2%2B1%29\"\r\n" );
document.write( "\r\n" );
document.write( "Write \"1%2Fx%5E3\" as \"x%5E%28-3%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"f%28x%29=%28x%5E2%2Bx%5E%28-3%29+%29%28x%5E3-x%5E2%2B1%29\"\r\n" );
document.write( "\r\n" );
document.write( "Multiply it out first:\r\n" );
document.write( "\r\n" );
document.write( "\"f%28x%29=%28x%5E2%2Bx%5E%28-3%29+%29%28x%5E3-x%5E2%2B1%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"f%28x%29=x%5E5-x%5E4%2Bx%5E2%2Bx%5E0-x%5E%28-1%29%2Bx%5E%28-3%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"f%28x%29=x%5E5-x%5E4%2Bx%5E2%2B1-x%5E%28-1%29%2Bx%5E%28-3%29\"\r\n" );
document.write( "\r\n" );
document.write( "Take the derivative of each term:\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%27%28x%29%22=5x%5E4-4x%5E3%2B2x%2Bx%5E%28-2%29-3x%5E%28-4%29\"\r\n" );
document.write( "\r\n" );
document.write( "Changing negative exponents to\r\n" );
document.write( "positive exponents in denominators.\r\n" );
document.write( "\r\n" );
document.write( "\"%22f%27%28x%29%22=+5x%5E4-4x%5E3%2B2x%2B1%2Fx%5E2-3%2Fx%5E4\"\r\n" );
document.write( "\r\n" );
document.write( "------------------------------------\r\n" );
document.write( "(b)  \"matrix%282%2C1%2C%22%22%2Cf%28x%29=+e%5E%28x%5E3%2B2x%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Rule:  copy it over and multiply by the derivative of the exponent:\r\n" );
document.write( "\r\n" );
document.write( "\"matrix%282%2C1%2C%22%22%2C%22f%27%28x%29%22=+e%5E%28x%5E3%2B2x%29%2A%283x%5E2%2B2%29%29\"\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );