document.write( "Question 1160094: Find f ' (x) if f(x)=(4x-5)^3 x (5x^2+8)^3 \n" ); document.write( "
Algebra.Com's Answer #783272 by math_helper(2461)\"\" \"About 
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\n" ); document.write( "Another way....\r
\n" ); document.write( "\n" ); document.write( "\"+f%28x%29+=+%284x-5%29%5E3%2A%285x%5E2%2B8%29%5E3+\"\r
\n" ); document.write( "\n" ); document.write( "Use the product & chain rules:\r
\n" ); document.write( "\n" ); document.write( "Product rule d(f(x)g(x))/dx = f(x)g'(x) + f'(x)g(x)\r
\n" ); document.write( "\n" ); document.write( "Example: f'( \"+%283x%2B2%29%282x%5E2%2B1%29+\") = \"+%283x%2B2%29%284x%29+%2B+%282x%5E2%2B1%29%283%29+\" and then simplify if necessary. Yes, that simple! \r
\n" ); document.write( "\n" ); document.write( "\"First times the derivative of the 2nd, plus the 2nd times the derivative of the first.\"\r
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\n" ); document.write( "\n" ); document.write( "Chain rule (f(g(x)))' = f'(g(x))*g'(x) \r
\n" ); document.write( "\n" ); document.write( "Example: f' ( \"+%283x%5E2%2B2%29%5E4+\" ) = \"+4%283x%5E2%2B2%29%5E3+%2A+%286x%29+\" \r
\n" ); document.write( "\n" ); document.write( "\"Derivative of the expression times the derivative of what's inside.\"\r
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\n" ); document.write( "\n" ); document.write( "f'(x) = \r
\n" ); document.write( "\n" ); document.write( "Factor out \"+%284x-5%29%5E2%2A%285x%5E2%2B8%29%5E2+\"
\n" ); document.write( " = \"+%284x-5%29%5E2%2A%285x%5E2%2B8%29%5E2+%2A+%28180x%5E2-150x%2B96%29+\"
\n" ); document.write( " = \"+highlight+%286%2A%284x-5%29%5E2%2A%285x%5E2%2B8%29%5E2+%2A+%2830x%5E2-25x%2B16%29+%29+\"\r
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