Differentiate how? Part 3

Calculus Level 1

$\huge y=e^{x + e^{x + e^{x + e^{x + \cdots }}}}$

Let $y$ denote the infinite power tower function as described above.

Determine the value of $\frac{dy}{dx}$ in terms of $y$ .

\frac { y+1 }{ 1-y }

\frac { y }{ 1-y }

\frac { 2y }{ 1-y }

\frac { 1 }{ 1-y }

2 solutions

Raj Rajput
Aug 15, 2015

Adrabi Abderrahim
Aug 29, 2015

we've $y={ e }^{ x+{ e }^{ x+...\infty } }$

then $\frac { dy }{ dx } =( \frac { d }{ dx }(x + { e }^{ x+{ e }^{ x+...\infty } })) y = ( \frac { d }{ dx }(x + y)) y = ( 1 + \frac { dy }{ dx }) y$

$\Rightarrow \frac { dy }{ dx } (1-y) = y \Rightarrow \frac { dy }{ dx } = \frac { y }{ 1-y }$

Differentiate how? Part 3

2 solutions

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