Question

If x = 2t/1+t², y=1-t²/1+t², then dy/dx=.........,Select Proper option from the given options.
(a) 2t²/1-t²
(b) 2t/1+t²
(c) 2t
(d) -2t/1-t²

Answer 1

x = 2t/( 1 + t²)

differentiate with respect to t,

dx/dt = d{2t/(1 + t²)}/dt

= {(1 + t²) × 2 - 2t × 2t }/(1 + t²)²

= {2(1 + t²) - 4t²}/(1 + t²)²

=2(1 - t²)/(1 + t²)²


similarly, y = (1 - t²)/(1 + t²)

differentiate with respect to t,

dy/dt = d{(1 - t²)/(1 + t²)}/dt

= {(1 + t²) × -2t - (1 - t²) × 2t }/(1 + t²)²

= {-2t - 2t³ - 2t + 2t³ }/(1 + t²)²

= -4t/(1 + t²)²


so, dy/dx = {dy/dt}/{dx/dt}

= {-4t/(1 + t²)²}/{2(1 - t²)/(1 + t²)²}

= -2t/(1 - t²)

hence, option (d) is correct.

Answer 2

In the attachment I have answered this problem.                         I have applied parametric differentiation to find derivative of the given parametric functions.                             See the attachment for detailed solution.