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x= exp(tan^-1(y-x^2)/x^2 then dy/dx notex^2 means x square

x= exp(tan^-1(y-x^2)/x^2 then dy/dx


notex^2 means  x square

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2 Answers

student iit
18 Points
14 years ago

Take natural logarithm both sides and solve.

Proceed using the method , I will help you along.

Badiuddin askIITians.ismu Expert
148 Points
14 years ago

x= exp(tan^-1(y-x^2)/x^2)

first simplyfy this

take log both side

lnx =tan^-1(y-x^2)/x^2

or tan(lnx)=(y-x^2)/x^2

or 1+tan(lnx) =y/x2

or y= x2 +x2tan(lnx)

now differntiate

dy/dx=2x +x sec2(lnx) +2x tan(lnx)

that is tha final answer


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