exponential function

Calculus Tutorial

exponential function

Intro

y=v(u(x)) — dy/dx=v'(u(x)).u'(x)
(1) d/dx(sinx)=cosx
(2) d/dx(cosx)=-sinx
(3) d/dx(tanx)=(secx)2

Sample Problem

y=e(tanx).sin(e)(x2+2x+1)
find dy/dx

Solution

y=e(tanx).sin((e)(x2+2x+1))
dy/dx=d/dx(e(tanx).sin(e)(x2+2x+1))
dy/dx=e(tanx).d/dx(sin(e)(x2+2x+1))+sin(e)(x2+2x+1).d/dx(e(tanx)) — product rule
d/dx(sin(e)(x2+2x+1)=cos(e)(x2+2x+1).e(x2+2x+1).(2x+2) — chain rule
d/dx((e)tanx)=e(tanx).(secx)2 — chain rule
dy/dx=e(tanx).cos(e)(x2+2x+1).e(x2+2x+1).(2x+2)+sin(e)(x2+2x+1).e(tanx).(secx)2 — substitute



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