Question

$\begin{gathered}\bigstar\:\:\underline{ \red{\sf QueStion : }} \bigstar \\\end{gathered}$
$\bf 1) \: y = log \sqrt{ {9x}^{2} + 10x + 8 }$
$\bf 2) \: y = \frac{ \sqrt{5x + 6} }{ \sqrt{4x - 5} }$
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Answer 1

$\underline{\underline{\maltese\: \: \textbf{\textsf{Answer}}}}$

★ Question 1.

$\sf y = log \sqrt{ {9x}^{2} + 10x + 8}$

Diffe. w. r. to x

$\sf \longrightarrow \frac{dy}{dx} = \frac{1}{ \sqrt{ {9x}^{2} + 10x + 8 } } \times \frac{1}{2 \sqrt{ {9x}^{2} + 10x + 8} } \times (9 \times 2x + 10 \times 1)$

$\sf \longrightarrow \frac{dy}{dx} = \frac{18x + 10}{2( {9x}^{2} + 10x + 8}$

$\sf \longrightarrow \frac{dy}{dx} = \frac{ \cancel2(9x + 5)}{ \cancel2( {9x}^{2} + 10x + 8) }$

$\sf \longrightarrow \frac{dy}{dx} = \frac{(9x + 5)}{( {9x}^{2} + 10x + 8) }$ㅤ

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★ Question 2.

$\sf y = \frac{ \sqrt{5x + 6} }{ \sqrt{4x - 5} }$

Diff. w. r. to x,

$\sf \longrightarrow \frac{dy}{dx} = \frac{ \sqrt{4x - 6} \frac{d}{dx}( \sqrt{5x + 6)} - (5x + 6) \frac{d}{dx} \sqrt{4x - 5}}{ {( \sqrt{4x - 5)} }^{2} }$

$\sf \longrightarrow \frac{dy}{dx} = \frac{ \sqrt{(4x - 5)} \times \frac{1 \times (5 \times 1 + 0)}{2 \sqrt{5x} + 6} - \sqrt{5x + 6} \frac{1 \times (4 \times 1 - 0)}{2 \sqrt{4x - 5} } }{ {( \sqrt{4x - 5)} }^{2} }$

$\sf \longrightarrow \frac{ \frac{\sqrt{4x - 5} \times 5}{2 \sqrt{5x + 6}} - \frac{\sqrt{(5x + 6)} \times 4}{2 \sqrt{4x - 5} } }{{(4x - 5)} }$

$\sf \longrightarrow \frac{5(4x - 5) - 4 \times (5x + 6)}{2 \sqrt{4x - 5} \sqrt{5x + 6} (4x - 5) }$

$\sf \longrightarrow \frac{dy}{dx} = \frac{20x - 25 - 20x - 24}{2(4x - 5) \frac{3}{2 \sqrt{5x + 6} }}$

$\sf \longrightarrow \frac{dy}{dx} = \frac{ - 49}{2(4x - 5) \frac{3}{2 \sqrt{5x + 6} } }$

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Hope it helps

__________thanx

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Answer 2

hope it helps u

THANKS(¬_¬)ﾉ