Question

How do you use the power rule to differentiate `f(x)=1-x^2+3x^3sqrtx`?

Answer 1

`f'(x)=21/2sqrt(x^5)-2x`

Explanation:

differentiate using the `color(blue)"power rule"` on each term.

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

Express `3x^3sqrtx=3x^3.x^(1/2)=3x^(7/2)`

`f(x)=1-x^2+3x^(7/2)`

`rArrf'(x)=0-2x+21/2x^(5/2)`

`=21/2sqrt(x^5)-2x`