Question

differentiate √x cosec(5x + 7)​

Answer 1

Answer:

$\frac{dy}{dx} =(cosec(5x+7))(\frac{1}{2\sqrt{x}} -5\sqrt{x} cot(5x+7))$

Step-by-step explanation:

Use the product rule.

let  $u=\sqrt{x}$  ⇒  $\frac{du}{dx}=\frac{1}{2\sqrt{x}}$

let  $v=cosec(5x+7)$  ⇒  $\frac{dv}{dx} =-5cot(5x+7)cosec(5x+7)$  

$\frac{dy}{dx} =u\frac{dv}{dx} +v\frac{du}{dx}$

    $=-5\sqrt{x} cot(5x+7)cosec(5x+7)+\frac{1}{2\sqrt{x}} cosec(5x+7)$

      $=(cosec(5x+7))(\frac{1}{2\sqrt{x}} -5\sqrt{x} cot(5x+7))$