Question

If $x=\frac{e^t+e^{-t}}{2},y=\frac{e^t-e^{-t}}{2}$, then $\frac{dx}{dy}=$

• A. $-\frac{x}{y}$
• B. $\frac{y}{x}$
• C. $\frac{x}{y}$
• D. $-\frac{y}{x}$

Answer 1

Answer: (B)

$\frac{y}{x}$

$x=\frac{e^t+e^{-t}}{2},$ $y=\frac{e^t-e^{-t}}{2}$

$\Rightarrow \frac{dx}{dt}=\frac{e^t-e^{-t}}{2}=y,\frac{dy}{dt}=\frac{e^t+e^{-t}}{2}=x$

$\Rightarrow \frac{dx}{dy}=\frac{dx}{dt}\times \frac{dt}{dy}$

$=y\times \frac{1}{x}$

$=\frac{y}{x}$

Hence, the answer is $\frac{y}{x}.$