If y = log √x + √x^2 + a^2 then dy/...
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If ( y=log sqrt{x+sqrt{x^{2}+a^{2}}} ) then ( d y / d x ) is

JEE/Engineering Exams
Maths
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If y = log √x + √x^2 + a^2 then dy/dx is
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( y=log sqrt{x+sqrt{x^{2}+a^{2}}} )
( y=frac{1}{2} log (x+sqrt{x^{2}+a^{2}}) Rightarrow 2 y=log (x+sqrt{x^{2}+a^{2}}) )
( frac{a d y}{d x}=left(frac{1}{x+sqrt{x^{2}+a^{2}}}right)left(1+frac{2 x}{2 sqrt{x^{2}+a^{2}}}right) )
( frac{d y}{d x}=left(frac{1}{x+sqrt{x^{2}+a^{2}}}right)left(frac{x+sqrt{x^{2}+a^{2}}}{sqrt{x^{2}+a^{2}}}right) )
( frac{d y}{d x}=frac{1}{2 sqrt{x^{2}+a^{2}}} )

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