Question

Use the quotient rule to differentiate.

Formula:- dy/dx = (v×du/dx - u×dv/dx)/v^2

Answer:- 2x - 9/(4x + 3)^3/2

Help me please​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\sf{y=\dfrac{x+6}{\sqrt{4x+3}}}$

$\sf{\implies\dfrac{dy}{dx}=\dfrac{\sqrt{4x+3}\cdot\dfrac{d}{dx}(x+6)-(x+6)\cdot\dfrac{d}{dx}\big(\sqrt{4x+3}\big)}{\left(\sqrt{4x+3}\right)^2}}$

$\sf{\implies\dfrac{dy}{dx}=\dfrac{\sqrt{4x+3}\cdot1-(x+6)\cdot\dfrac{4}{2\sqrt{4x+3}}}{4x+3}}$

$\sf{\implies\dfrac{dy}{dx}=\dfrac{\sqrt{4x+3}-\dfrac{2(x+6)}{\sqrt{4x+3}}}{4x+3}}$

$\sf{\implies\dfrac{dy}{dx}=\dfrac{\dfrac{\left(\sqrt{4x+3}\right)^2-2(x+6)}{\sqrt{4x+3}}}{4x+3}}$

$\sf{\implies\dfrac{dy}{dx}=\dfrac{4x+3-2x-12}{(4x+3)\sqrt{4x+3}}}$

$\sf{\implies\dfrac{dy}{dx}=\dfrac{2x-9}{\left(4x+3\right)^{\frac{3}{2}}}}$