Question

How do you find the derivative of `q(r)=r^3cosr`?

Answer 1

`q'(r)=3r^2cosr-r^3sinr`

Explanation:

differentiate using the `color(blue)"product rule"`

`"Given " q(r)=f(r).g(r)" then"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(q'(r)=f(r)g'(r)+g(r)f'(r))color(white)(2/2)|)))larr" product rule"`

`"here " f(r)=r^3rArrf'(r)=3r^2`

`"and " g(r)=cosrrArrg'(r)=-sinr`

`rArrq'(r)=r^3(-sinr)+cosr.3r^2`

`=3r^2cosr-r^3sinr`