Let u(x)=x9\displaystyle {u}{\left({x}\right)}={x}^{{9}}, v(x)=cos⁡x\displaystyle {v}{\left({x}\right)}={\cos{{x}}} and f(x)=u(x)v(x)\displaystyle {f{{\left({x}\right)}}}={u}{\left({x}\right)}{v}{\left({x}\right)}.

u′(x)\displaystyle {u}'{\left({x}\right)} =  

v′(x)=−sin⁡(x)\displaystyle {v}'{\left({x}\right)}=-{\sin{{\left({x}\right)}}}.

f(x)=u(x)v(x)\displaystyle {f{{\left({x}\right)}}}={u}{\left({x}\right)}{v}{\left({x}\right)} =  

f′(x)=u′(x)v(x)+u(x)v′(x)\displaystyle {f}'{\left({x}\right)}={u}'{\left({x}\right)}{v}{\left({x}\right)}+{u}{\left({x}\right)}{v}'{\left({x}\right)} =  

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