Question

If \(f(x)\) is a differentiable function and \[ y=e^{f(x)+e^{f(x)+e^{f(x)+\cdots \infty}}}, \] then \[ \frac{dy}{dx}= \ ? \]

• A. \(\dfrac{yf'(x)}{1+y}\)
• B. \(\dfrac{(1+y)f'(x)}{y}\)
• C. \(\dfrac{(1-y)f'(x)}{y}\)
• D. \(\dfrac{yf'(x)}{1-y}\)

Hint:

Whenever an expression repeats infinitely, assign it a variable and use self-similarity to create an equation.

Answer 1

The Correct Option is D