Question

if y=sin (4x+2π/3)then the value of dy/dx is
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Answer 1

$\sf y=sin\bigg(4x+\dfrac{2\pi}{3}\bigg)$

Differentiate with respect to x on both sides ,

$\to \sf \dfrac{dy}{dx}=\dfrac{d}{dx}\bigg[sin\bigg(4x+\dfrac{2\pi}{3}\bigg)\bigg]$

• d/dx ( sin x ) = cos x

$\sf \to \dfrac{dy}{dx}=cos\bigg(4x+\dfrac{2\pi}{3}\bigg)\dfrac{d}{dx}\bigg(4x+\dfrac{2\pi}{3}\bigg)$

• d/dx ( constant ) = 0

$\to \sf \dfrac{dy}{dx}=cos\bigg(4x+\dfrac{2\pi}{3}\bigg)(4)\\\\\leadsto \sf \pink{\dfrac{dy}{dx}=4.cos\bigg(4x+\dfrac{2\pi}{3}\bigg)}\ \; \bigstar$

More Info :

• d/dx ( sin x ) = cos x
• d/dx ( cos x ) = - sin x
• d/dx ( tan x ) = sec²x
• d/dx ( cot x ) = - csc²x
• d/dx ( sec x ) = sec x . tan x
• d/dx ( csc x ) = - csc x . cot x