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The function is $\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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Derivative of a absolute function: $\"\"$ .

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$\"\"$

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The denominator of the function cannot be zero.

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$\"\"$ and $\"\"$ .

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$\"\"$ and $\"\"$ .

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The function is not defined when $\"\"$ and $\"\"$ .

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Therefore, the function is differentiable for all values except at $\"\"$ and $\"\"$ .

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Find the function in piecewise form.

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Definition of absolute function:

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If $\"\"$ , then $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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$\"\"$ is defined as

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If $\"\"$ , then $\"\"$ and $\"\"$ .

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Thus, $\"\"$ .

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$\"\"$ .

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If $\"\"$ , then $\"\"$ and $\"\"$ .

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Thus, $\"\"$ .

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$\"\"$ .

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If $\"\"$ , then $\"\"$ and $\"\"$ .

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Thus, $\"\"$ .

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Therefore, the function is defined as $\"\"$

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Find the derivative of the function.

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Find $\"\"$ when $\"\"$ :

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$\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Find $\"\"$ when $\"\"$ :

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$\"\"$

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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Find $\"\"$ when $\"\"$ :

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$\"\"$ .

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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The derivative of the function $\"\"$ .

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Graph:

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Graph of the function $\"\"$

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$\"\"$

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Graph the derivative function $\"\"$

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$\"\"$

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(a) The derivative of the function $\"\"$ .

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(b)

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Graph of the function is

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$\"\"$

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Graph of the derivative function is

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$\"\"$ .

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