If `a gt0, x=(t+(1)/(t))^(a) and y=a^((t+(1)/(t)))`, find `(dy)/(dx).`

Explanation

We have given

`x=(t+(1)/(t))^(a) and y=a^((t+(1)/(t)))`
Here

`frac{d y}{d x}=frac{frac{d y}{d t}}{frac{d x}{d t}}`

` y=a^((t+(1)/(t)))`

By differentiation

`frac{d y}{d t}=a^{(t+frac{1}{t})}cdot log a cdot frac{d (t+frac{1}{t})}{d t}`

`= a^{(t+frac{1}{t})}cdot log a cdot(1-frac{1}{t^2})`

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