Q14 of 45 Page 1

If y^x = e^{y – x}, prove that

Given, y^x = e^{y – x}

Taking log both sides –

⇒ x log y = (y – x) log_e e

⇒ x log y = y – x …(1)

⇒ y = x (1 + log y) …(2)

Differentiating w.r.t x, we get –

Applying product rule and chain rule of differentiation-

⇒

⇒ …[from eqn 1]

⇒ …[putting the value of y/x form (2)]

Show that:

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