$\"\"$

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Observe the figure.

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Rate of change in $\"\"$ is $\"\"$ .

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From pythagoras rule $\"\"$ .

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Substitute $\"\"$ in the above equation .

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$\"\"$

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$\"\"$ .

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From the figure $\"\"$

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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From the power rule of derivative: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Consider right angle triangle

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$\"\"$

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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From the power rule of derivative: $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ in the equation $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The horizontal change $\"\"$ .

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substitute $\"\"$ and $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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The horizontal change $\"\"$

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Vertical change $\"\"$

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$\"\"$

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$\"\"$

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Vertical change $\"\"$ .

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$\"\"$

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The rate of horizontal change $\"\"$ .

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The rate of Vertical change $\"\"$ .