document.write( "Question 817133: i am not sure what category to put this under, but what is the derivative of 10x - (3x^2/400)? \n" ); document.write( "

Algebra.Com's Answer #491915 by KMST(5328) $\"\"$ $\"About$

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Divide and conquer.
\n" ); document.write( "The derivative of $\"10x\"$ is $\"10\"$ multiplied times the derivative of $\"x\"$ , which is $\"1\"$ .
\n" ); document.write( "The derivative of $\"3x%5E2%2F400=%283%2F400%29x%5E2\"$ is $\"3%2F400\"$ times the derivative of $\"x%5E2\"$ , which is $\"2x\"$ .
\n" ); document.write( "So the derivative of $\"10x+-+3x%5E2%2F400\"$ is
\n" ); document.write( " $\"10-%283%2F400%29%282x%29=10-3x%2F200\"$
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\n" ); document.write( "HOW TO CALCULATE THE EASIER DERIVATIVES:
\n" ); document.write( "To calculate the derivative of a sum $\"f%28x%29+%2B+g%28x%29\"$ , where $\"f%28x%29\"$ and $\"g%28x%29\"$ are functions of your variable $\"x\"$ , you just add the derivatives of both functions.
\n" ); document.write( "The derivative of $\"a%2Ah%28x%29\"$ , where $\"a\"$ is any real number and $\"h%28x%29\"$ is a function of your variable $\"x\"$ is $\"a\"$ times the derivative of $\"f%28x%29\"$ .
\n" ); document.write( "The derivative of $\"x%5Ep\"$ , where $\"p\"$ is any real number and $\"x\"$ is your variable is $\"p%2Ax%5E%28p-1%29\"$ . This is so general that the derivative of $\"x%5E0=1\"$ is $\"0%2Ax%5E%28-1%29=0\"$ .
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\n" ); document.write( "NOTE:
\n" ); document.write( "10x - (3x^2/400) = 10x - 3x^2/400 = $\"10x+-+3x%5E2%2F400\"$
\n" ); document.write( "(Those parentheses were not needed, because order of operations conventions require that all multiplications/divisions be done before additions/subtractions). \n" ); document.write( "

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