How do you find the derivative of $e^{2 y}$ $e^(2y)$ ?

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Answer 1 · 2016-11-29T08:29:50

$\frac{d y}{d x} = \frac{1}{2 x}$ $dy/dx=1/(2x)$ Assuming: $x = e^{2 y}$ $x=e^(2y)$

This queston is somewhat ambigious as is does not state the variable which we are to find the derivitive with respect to.

I will assume: $x = e^{2 y}$ $x=e^(2y)$ and that we are seeking $\frac{d y}{d x}$ $dy/dx$

$x = e^{2 y}$ $x=e^(2y)$

$ln x = 2 y$ $lnx = 2y$

$y = \frac{1}{2} ln x$ $y=1/2lnx$

$\frac{d y}{d x} = \frac{1}{2} \cdot \frac{1}{x} = \frac{1}{2 x}$ $dy/dx = 1/2*1/x = 1/(2x)$

NB: If the question was intended to be: $\frac{d}{d y} [e^{2 y}]$ $d/dy[e^(2y)]$ the result would have been: $2 e^{2 y}$ $2e^(2y)$

How do you find the derivative of e^(2y)e2ye^(2y)?