Question

if x=tan^-1(e^t) y=sqrt(1+e^2t) then dy/dx=​

Answer 1

Answer:

$x= 1+t 2 2t​ , y= 1+t 2 1−t 2 ​ By differentiating w.r. to t, we getdtdx​ = (1+t 2 ) 2 ((1+t 2 ) dtd​ (2t)−2t dtd​ (1+t 2 ))​ And dtdy​ = (1+t 2 ) 2 ((1+t 2 ) dtd​ (1−t 2 )−(1−t 2 ) dtd​ (1+t 2 ))​ dtdx​ = (1+t 2 ) 2 (1+t 2 )2−2t×2t​ = (1+t 2 ) 2 2−2t 2 ​ dtdy​ = (1+t 2 ) 2 (1+t 2 )(−2t)−(1−t 2 )2t​ = (1+t 2 ) 2 −4t​ dxdy​​$

Step-by-step explanation: