document.write( "Question 1200824: Using the chain rule, show that the following statements are always true:\r
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Algebra.Com's Answer #835121 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "g(x) is an even function if and only if g(-x) = g(x)\r\n" );
document.write( "g(x) is an odd function if and only if g(-x) = -g(x)\r\n" );
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a) If f(x) is an odd function then f'(x) is an even function

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document.write( "Take derivatives of both sides:\r\n" );
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document.write( "Divide both sides by -1\r\n" );
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document.write( "So f'(x) is an even function.\r\n" );
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b) If f(x) is an even function then f'(x) is an odd function

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document.write( "Take derivatives of both sides:\r\n" );
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document.write( "Divide both sides by -1\r\n" );
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document.write( "So f'(x) is an odd function.\r\n" );
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document.write( "Edwin

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