Differentiating using multiple rule

Calculus Tutorial

Differentiating using multiple rule

Intro

using the chain rule and product rule

Sample Problem

y=cos((x3+2).sin(x+1))
find dy/dx

Solution

y=cos((x3+2).sin(x+1))
dy/dx=d/dx(cos((x3+2).sin(x+1))) — differentiate
dy/dx=(-sin(x3+2).sin(x+1)).d/dx((x3+2).sin(x+1)) — chain rule
dy/dx=(-sin(x3+2).sin(x+1)).(d/dx(x3+2).sin(x+1)+d/dx(sin(x+1)).(x3+2)) — product rule
dy/dx=-sin(x3+2).sin(x+1).(3×2.sin(x+1)+cos(x+1).1.(x3+2))
dy/dx=-sin(x3+2)sin(x+1)(3×2.sin(x+1)+(x3+2)cos(x+1)) — simplify



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