Find the dervaline of following cot...
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Find the dervaline of following cot' ve

Railway Exams
Maths
Solution
90
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As we know that [ begin{array}{c} frac{d}{d x}left(cot ^{-1} xright)=frac{-1}{1+x^{2}} cot ^{-1} sqrt{x} text { bt } sqrt{x}=y cot ^{-1} y frac{d}{d x}left(cot ^{-1} sqrt{x}right)=frac{d cot ^{-1} y}{d y} frac{d y}{d x} end{array} ] by chowin reale [ begin{array}{l} =frac{-1}{1+y^{2}} times frac{1}{2 sqrt{x}} =frac{-1}{1+(sqrt{x})^{2}+frac{1}{2 sqrt{x}}} =frac{-1}{2 sqrt{x}(1+x)} end{array} ]
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