Question

Differenciate the following :-
1)(3x^2 + 7) (6x + 3)
2) √(4x^2 - 7)​

Answer 1

Answer:

Explanation:

Here's your answer in the pic

Answer 2

Q. Differenciate the following :-

1)(3x^2 + 7) (6x + 3)

2) √(4x^2 - 7)

Explanation:-

$let \: y = (3 {x}^{2} + 7)(6x + 3)$

Using product rule we get,

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

$= (3 {x}^{2} + 7)(6 + 0) + (6x + 3)(6x + 0)$

$= 18 {x}^{2} + 42 \times 36 {x}^{2} + 18x$

$= 54 {x}^{2} + 18x + 42$

$2. \: \: y = \sqrt{4 {x}^{2} - 7}$

$= {(4 {x}^{2} - 7)}{ \frac{1}{2} }$

$using \: chain \: rule \:$

$\frac{dy}{dx} = \frac{1}{2} {(4 {x}^{2} - 7)}{ \frac{ - 1}{2} } \frac{d}{dx} (4 {x}^{2} - 7)$

$= \frac{1}{2} {(4 {x}^{2} - 7)}{ \frac{ - 1}{2} }(8x - 0)$

$= \frac{4x}{ \sqrt{4 {x}^{2} - 7} }$