Question

y = sinx cos3x find dy/dx​

Answer 1

Answer:

$\displaystyle{\boxed{\red{\sf\:\dfrac{dy}{dx}\:=\:\cos\:x\:.\:\cos\:3x\:-\:3\:\sin\:3x\:.\:\sin\:x}}}$

Step-by-step-explanation:

The given function is

$\displaystyle{\sf\:y\:=\:\sin\:x\:\cos\:3x}$

We have to find the derivative of the given function.

Now,

$\displaystyle{\sf\:y\:=\:\sin\:x\:\cos\:3x}$

We know that,

If

$\displaystyle{\sf\:y\:=\:uv}$

then

$\displaystyle{\boxed{\pink{\sf\:\dfrac{dy}{dx}\:=\:\dfrac{du}{dx}\:v\:+\:\dfrac{dv}{dx}\:u}}}$

Now, we have,

$\displaystyle{\sf\:y\:=\:\sin\:x\:\cos\:3x}$

$\displaystyle{\sf\:u\:=\:\sin\:x\:\&\:v\:=\:\cos\:3x}$

$\displaystyle{\implies\sf\:\dfrac{dy}{dx}\:=\:\left(\:\dfrac{d}{dx}\:(\sin\:x)\:\right)\:\cos\:3x\:+\:\left(\:\dfrac{d}{dx}\:(\cos\:3x)\:\right)\:\sin\:x}$

$\displaystyle{\implies\sf\:\dfrac{dy}{dx}\:=\:\cos\:x\:.\:\cos\:3x\:+\:\left(\:\dfrac{d}{dx}\:(\:\cos\:3x\:)\:\right)\:\left(\:\dfrac{d}{dx}\:(3x)\:\right)\:\sin\:x}$

$\displaystyle{\implies\sf\:\dfrac{dy}{dx}\:=\:\cos\:x\:.\:\cos\:3x\:+\:(\:-\:\sin\:3x\:)\:3\:.\:\sin\:x}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:\dfrac{dy}{dx}\:=\:\cos\:x\:.\:\cos\:3x\:-\:3\:\sin\:3x\:.\:\sin\:x}}}}$