Question

How do you find the derivative of `S(r)=9r^2+3tanr`?

Answer 1

`S'(r)=18r+3sec^2r`

Explanation:

differentiate the first term using the `color(blue)"power rule"` and use the `color(blue)"standard derivative for tan"`

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(ax^n)=nax^(n-1))color(white)(2/2)|)))" power rule"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(tanx)=sec^2x)color(white)(2/2)|)))`

`S(r)=9r^2+3tanr`

`rArrS'(r)=18r+3sec^2r`