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`(1)/(f(t)^(2))``-(g(t))^(2)``(-g(t))/f(t)``(-f(t))/(g(t))`

Solution :

`x=f(t)=a^(In(b))=a^(t" In "b)" (1)"` <br> `y=g(t)=b^(-In(a^(t)))=(b^(In a))^(-t)=(a^(In b))^(-t)=a^(-t" In b")` <br> `therefore" "y=g(t)=a^(In(b^(-t)))=f(-t)" (2)"` <br> From equations (1), and (2), <br> `xy=1` <br> `y=(1)/(x)` <br> `therefore" "(dy)/(dx)=-(1)/(x^(2))=-(1)/(f^(2)(t))` <br> `"Also, "xy=1 rArr-(1)/(f^(2)(t))=-g^(2)(t)` <br> `therefore" "(dy)/(dx)=-(1)/(x^(2))=-(y^(2))/(1)` <br> `"Also, "xy=1 rArr(dy)/(dx)=-(y)/(x)=-(g(t))/(f(t))`