Composite exponential function differentiation

Calculus Tutorial

Composite exponential function differentiation

Intro

product rule
chain rule
ln(a)m=m(ln)a

Sample Problem

y=(sin(x))x
find dy/dx

Solution

y=(sin(x))x
ln(y)=ln(sinx)x take(ln) both side
ln(y)=x.ln(sinx) ln(a)m=m.ln(a)
d/dx(ln(y))=d/dx(x.ln(sinx)) take derivative both side
1/y.dy/dx=1.ln(sinx)+(1/sinx).cosx.x product rule
d/dx(ln(sinx))=(1/sinx).cosx chain rule
dy/dx=y.(ln(sinx)+x.cosx/sinx) multiply by y both side
=(sin(x))x.(ln(sinx)+x.cosx/sinx) substituting y
=(sin(x))x.(ln(sinx)+x.cot(x)) simplify



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