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Tanzania [10]
3 years ago
8

Find the derivative of |x|/(x-1)

Mathematics
1 answer:
ki77a [65]3 years ago
4 0
\bf \cfrac{|x|}{x-1}\iff \cfrac{\sqrt{x^2}}{x-1}\iff \cfrac{(x^2)^{\frac{1}{2}}}{x-1}
\\\\\\
\textit{using the quotient rule}
\\\\\\
\cfrac{dy}{dx}=\cfrac{\frac{1}{2}(x^2)^{-\frac{1}{2}}\cdot 2x(x-1)-(x^2)^{\frac{1}{2}}\cdot 1}{(x-1)^2}

\bf \cfrac{dy}{dx}=\cfrac{\frac{x(x-1)-(x^2)^{\frac{1}{2}}}{(x^2)^{\frac{1}{2}}}}{(x-1)^2}\implies \cfrac{dy}{dx}=\cfrac{x(x-1)-(x^2)^{\frac{1}{2}}}{(x^2)^{\frac{1}{2}}(x-1)^2}
\\\\\\\cfrac{dy}{dx}=\cfrac{x(x-1)-|x|}{|x|(x-1)^2}
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The area of a racquetball court is 800 square feet.The length of a standard court is twice as its width. What are the dimensions
zubka84 [21]

Given - area of a racquet ball court is 800 square feet.

length is the twice of the width

find out thedimensions of the racquet ball court.

To proof -

Formula

area of a rectangle = length×breadth

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let assume width be w

than  length become 2w

put in the formula

w×2w = 800 ft²

2w² = 800 ft²

w = \sqrt{400} ft

w = 20 ft

Than the length become 40 ft.

Hence proved


3 0
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