What is the derivative of $e^{2 x y}$ $e^(2xy)$ ?

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Answer 1 · 2017-04-06T14:27:33

$\frac{d}{d x} (e^{2 x y})$ $d/dx(e^(2xy))$ or $\frac{d}{d t} (e^{2 x y})$ $d/dt(e^(2xy))$

With respect to $x$ $x$
$\frac{d}{d x} (e^{2 x y}) = (e^{2 x y}) \frac{d}{d x} (2 x y)$ $d/dx(e^(2xy)) = (e^(2xy)) d/dx(2xy)$

$= (e^{2 x y}) (2 y + 2 x \frac{d y}{d x})$ $= (e^(2xy)) (2y+2x dy/dx)$

With respect to $t$ $t$
$\frac{d}{d t} (e^{2 x y}) = (e^{2 x y}) \frac{d}{d t} (2 x y)$ $d/dt(e^(2xy)) = (e^(2xy)) d/dt(2xy)$

$= (e^{2 x y}) (2 y \frac{d x}{d t} + 2 x \frac{d y}{d x})$ $= (e^(2xy)) (2ydx/dt + 2x dy/dx)$

What is the derivative of e^(2xy)e2xye^(2xy)?