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Higher Order Derivatives

Find the valu...

Question

Find the value of $9^{y} + 3^{y + 1}$ if $x = 3^{y}$ and $x$ and $y$ are both integers.

A

x^{3}

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B

3 x + 3

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C

x (x + 3)

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D

x^{2} + 3

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Solution

The correct option is C $x (x + 3)$
Given, $x = 3^{y}$
$9^{y} + 3^{y + 1} = (3^{2})^{y} + 3^{y} \cdot 3^{1}$
$= 3^{2 y} + 3 x$
$= (3^{y})^{2} + 3 x$
$= x^{2} + 3 x$
$= x (x + 3)$

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