document.write( "Question 1203615: Could you please help me with this Calculus problem? I am finding this problem hard to solve. After a few steps, I am stuck and don't know how to proceed to find the derivative.\r
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Algebra.Com's Answer #839313 by math_helper(2461)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "h(x) = \"+%283x-12%29%285x%5E4-sqrt%28x%29%29%28e%5Ex%29+\"\r
\n" ); document.write( "\n" ); document.write( "The product rule can be applied:\r
\n" ); document.write( "\n" ); document.write( "If h(x) = A(x)B(x) then
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\n" ); document.write( " h'(x) = A(x)B'(x) + B(x)A'(x)\r
\n" ); document.write( "\n" ); document.write( "Choosing A(x) = (3x-12) and B(x) = \"+%285x%5E4-sqrt%28x%29%29%28e%5Ex%29+\"\r
\n" ); document.write( "\n" ); document.write( " A'(x) = 3\r
\n" ); document.write( "\n" ); document.write( "Unfortunately, B'(x) will be messy:
\n" ); document.write( " B'(x) = \r
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\n" ); document.write( "\n" ); document.write( "Now you have:
\n" ); document.write( " h'(x) = + \"+%285x%5E4-sqrt%28x%29%29%28e%5Ex%29%2A3+\"\r
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\n" ); document.write( "\n" ); document.write( "Expand the first term, combine like-terms, and pull out \"e%5Ex\", and you should get:\r
\n" ); document.write( "\n" ); document.write( " h'(x) = \r
\n" ); document.write( "\n" ); document.write( "[ Sometimes writing \"sqrt%28x%29+\" as x^(1/2) makes the workout easier. ]\r
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\n" ); document.write( "EDIT 9/14/23: tutor greenestamps answer is missing a factor of \"e%5Ex\"
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