Question

y=(3x2+7)(6x+3),find dy/dx ​

Answer 1

SOLUTION

GIVEN

$\displaystyle\sf{y = \frac{3 {x}^{2} + 7 }{6x + 3} }$

TO DETERMINE

$\displaystyle\sf{ \frac{dy}{dx} }$

EVALUATION

Here the given function is

$\displaystyle\sf{y = \frac{3 {x}^{2} + 7 }{6x + 3} }$

Now Differentiating both sides with respect to x we get

$\displaystyle\sf{ \frac{dy}{dx} = \frac{(6x + 3)\frac{d}{dx}(3 {x}^{2} + 7 ) - (3 {x}^{2} + 7)\frac{d}{dx}(6x + 3) }{{(6x + 3)}^{2} } }$

$\displaystyle\sf{ \implies \: \frac{dy}{dx} = \frac{(6x + 3) \times 6x - (3 {x}^{2} + 7) \times 6}{{(6x + 3)}^{2} } }$

$\displaystyle\sf{ \implies \: \frac{dy}{dx} = \frac{36 {x}^{2} + 18x - 18 {x}^{2} - 42}{{(6x + 3)}^{2} } }$

$\displaystyle\sf{ \implies \: \frac{dy}{dx} = \frac{18 {x}^{2} + 18x - 42}{{(6x + 3)}^{2} } }$

FINAL ANSWER

$\boxed{ \: \displaystyle\sf{ \frac{dy}{dx} = \frac{18 {x}^{2} + 18x - 42}{{(6x + 3)}^{2} } } \: }$