If y=e^sin inverse(t^2-1) and x=e^sec inverse(1/t^2-1), then dy/dx equal to:
-x/y; y/x; -y/x; x/y.

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If y=e^sin inverse(t^2-1) and x=e^sec inverse(1/t^2-1), then dy/dx
equal to:
-x/y; y/x; -y/x; x/y

Neha Sethi · Accepted Answer

Dear student
We have, y=esin-1t2-1On differentaiting, we getdydt=esin-1t2-1
ddtsin-1t2-1=11-t2-12 ddtt2-1
esin-1t2-1=ddtt2+ddt-1esin-1t2-11-t2-12=2tesin-1t2-11-t2-12      
(1)and x=esec-11t2-1On differentaiting, we getdxdt=esec-11t2-1
ddtsec-11t2-1=11-11t2-121t2-12 ddt1t2-1
esec-11t2-1=-ddtt2-1t2-12t2-12esec-11t2-11-t2-12=-2tesec-11t2-11-t2-12     
(2)Now, dydx=dy/dtdx/dt=2tesin-1t2-11-t2-12-2tesec-11t2-11-t2-12=esin-1t2-1-esec-11t2-1=-yx
Regards

If y=e^sin inverse(t^2-1) and x=e^sec inverse(1/t^2-1), then dy/dx equal to: -x/y; y/x; -y/x; x/y.

If y=e^sin inverse(t^2-1) and x=e^sec inverse(1/t^2-1), then dy/dx equal to:
-x/y; y/x; -y/x; x/y.