$\"\"$

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The function values are $\"\"$ and $\"\"$ .

\

Find $\"\"$ .

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(a)

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The function is $\"\"$ .

\

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

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$\"\"$

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Apply product rule of differentiation: $\"\"$ .

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$\"\"$

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Substitute $\"\"$ .

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$\"\"$

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

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$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

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(b)

\

The function is $\"\"$ .

\

Find $\"\"$ .

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$\"\"$

\

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

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$\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

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

\

$\"\"$

\

$\"\"$

\

It is not possible to calculate $\"\"$ ,if $\"\"$ is unknown.

\

The value of $\"\"$ is required.

\

$\"\"$

\

(c)

\

The function is $\"\"$ .

\

Find $\"\"$ .

\

$\"\"$

\

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

\

$\"\"$

\

Apply quotient rule of differentiation: $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

(d)

\

The function is $\"\"$ .

\

Find $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

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

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$ .

\

$\"\"$

\

(a) $\"\"$ .

\

(b) It is not possible to calculate $\"\"$ ,if $\"\"$ is unknown.

\

The value of $\"\"$ is required.

\

(c) $\"\"$ .

\

(d) $\"\"$ .