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  • If t(1+x^2) =x and x^2 +t^2 =y then at x=2 , then the value of dy/dx is

If t(1+x^2) =x and x^2 +t^2 =y then at x=2 , then the value of dy/dx is

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Solution:  We have ,    t(1+x^2)=x   and  y=x^2+t^2

               Rightarrow                            fracmathrmd ymathrmd x=(2x+2t)cdot fracmathrmd tmathrmd x

                 Also               t=fracx1+x^2

              herefore                       fracmathrmd tmathrmd x=frac1-x^2(1+x^2)^2    Now putting  x=2 ,we get 

           Rightarrow                  fracmathrmd tmathrmd x=-frac325

            herefore                     fracmathrmd ymathrmd x=2(2)+2(frac25)cdot (-frac325)=frac488125.

Posted by

Deependra Verma

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