product rule

Calculus Tutorial

product rule

Intro

product rule :(f(x)g(x))’=f(x)g'(x)+g(x)f'(x)
differentiating trigonometric functions: d/dx(sin(x))=cos(x), d/dx(cos(x)=-sin(x)
differentiating logarithmic function: d/dx(ln(x))=1/x

Sample Problem

f(x)=ln(x)sin(x)
find f'(x).

Solution

f(x)=ln(x)sin(x)
f'(x)=d/dx(ln(x)sin(x))
=ln(x).d/dx(sin(x))+sin(x).d/dx(ln(x)) product rule
=ln(x).cos(x)+sin(x).1/x differentiate ln(x) and sin(x)
=ln(x)cos(x)+sin(x)/x



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