Differentiating using multiple rules

Intro

We will need to use the product rule and chain rule

Sample Problem

Solution

Y=2×3√(3×2+1)
dy/dx=d/dx(2×3√(3×2+1)) — differentiate
=d/dx(2×3). √(3×2+1)+d/dx√(3×2+1).2×3 — product rule
=6×2. √(3×2+1)+1/2.(1/√(3×2+1)).6x.2×3 — chain rule and power rule
=6×2. √(3×2+1)+12×4/(2√(3×2+1)) — simplify
=(12×2(3×2+1)+12×4)/( 2√(3×2+1))