d/dx(sqrt(log(x+5)))\n | The derivative of f(x) is f\'(x.."/>
Posted by: raju161 March 20, 2010
derivatives - math problem help
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d/dx(f(x) = sqrt(log(x+5))) = (f\'(x) = 1/(2 (x+5) <br> sqrt(log(x+5))))


Possible derivation:\nd/dx(f(x)) = <br> d/dx(sqrt(log(x+5)))\n | The derivative of f(x) is f\'(x):\n= | f\'(x) = <br> d/dx(sqrt(log(x+5)))\n | Use the chain rule, d/dx(sqrt(log(x+5))) = ( <br> dsqrt(u))/( du) ( du)/( dx), where u = log(x+5) and ( dsqrt(u))/( du) = <br> 1/(2 sqrt(u)):\n= | f\'(x) = (d/dx(log(x+5)))/(2 sqrt(log(x+5)))\n | Use <br> the chain rule, d/dx(log(x+5)) = ( dlog(u))/( du) ( du)/( dx), where u = <br> x+5 and ( dlog(u))/( du) = 1/u:\n= | f\'(x) = (d/dx(x+5))/(2 (x+5) <br> sqrt(log(x+5)))\n | Differentiate the sum term by term:\n= | f\'(x) = <br> (d/dx(5)+d/dx(x))/(2 (x+5) sqrt(log(x+5)))\n | The derivative of 5 is <br> zero:\n= | f\'(x) = (d/dx(x))/(2 (x+5) sqrt(log(x+5)))\n | The <br> derivative of x is 1:\n= | f\'(x) = 1/(2 (x+5) sqrt(log(x+5)))
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