How do you differentiate $x y = \frac{π}{6}$ $xy=pi/6$ ?

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How do you differentiate $x y = \frac{π}{6}$ $xy=pi/6$ ?

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Answer 1 · 2017-01-31T13:58:31

$\frac{d y}{d x} = - \frac{y}{x}$ $dy/dx=-y/x$

Explanation:

differentiate $implicitly with respect to x$ $color(blue)"implicitly with respect to x"$

Using the $product rule$ $color(blue)"product rule"$ to differentiate the term xy

#rArr(x.dy/dx)+(y.d/dx(x))=0#

$\Rightarrow x \frac{d y}{d x} + y = 0 \Rightarrow x \frac{d y}{d x} = - y$ $rArrxdy/dx+y=0rArrxdy/dx=-y$

$\Rightarrow \frac{d y}{d x} = - \frac{y}{x}$ $rArrdy/dx=-y/x$

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How do you differentiate $x y = \frac{π}{6}$ $xy=pi/6$ ?

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