document.write( "Question 1156570: Find the derivative of the function, Solution or Explanation
\n" ); document.write( "y = (tan^−1(4x))^2 \n" ); document.write( "

Algebra.Com's Answer #779390 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " $\"y+=+%28tan%5E-1%284x%29%29%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( "apply the chain rule : $\"df%28u%29%2Fdx=%28df%2Fdu%29%2A+%28du%2Fdx%29\"$ \r
\n" ); document.write( "\n" ); document.write( "where $\"f=u%5E2\"$ and $\"u=tan%5E-1%284x%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"df%28u%29%2Fdx=%28d%2Fdu%29%28u%5E2%29%2A+%28du%2Fdx%29%28tan%5E-1%284x%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28d%2Fdu%29%28u%5E2%29=2u\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"%28du%2Fdx%29%28tan%5E-1%284x%29%29=4%2F%2816x%5E2%2B1%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"df%28u%29%2Fdx=y\"$ '\r
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\n" ); document.write( "\n" ); document.write( " $\"y\"$ '= $\"2u%2A+%284%2F%2816x%5E2%2B1%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "substitute back $\"u=tan%5E-1%284x%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y\"$ '= $\"2tan%5E-1%284x%29%2A+%284%2F%2816x%5E2%2B1%29%29\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y\"$ '= $\"%288tan%5E-1%284x%29%29%2F%2816x%5E2%2B1%29%29\"$ \r
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