Question

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

JEE/Engineering Exams

Maths

Solution

4.0 (1 ratings)

If y = log √x + √x^2 + a^2 then dy/dx is

( 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}}} )