Question

find the first derivative of ((x^3)/3)-x^2

Answer 1

\[y=\frac{ x^3 }{ 3 }-x^2\]
\[\frac{ d }{ dx }\left( a x^n \right)=a*nx ^{n-1}\]

Answer 2

yes, term by term. apply the power rule:

Answer 3

wouldn't you have to use the quotient rule?

Answer 4

no

Answer 5

you re multiplying x^2 times 1/3

Answer 6

I mean x63 times 1/3

Answer 7

x^3*

Answer 8

\(\large\color{slate}{ \displaystyle \frac{d}{dx}\left[ \frac{x^3}{3}- x^2\right]~~~\Rightarrow~~~ \frac{d}{dx}\left[ \frac{x^3}{3}\right]- \frac{d}{dx}\left[ x^2\right]\\ ~~\\~~\\ \displaystyle ~~~\Rightarrow~~~ 3\cdot\frac{d}{dx}\left[ x^3\right]~~~+~~~(-1)\cdot \frac{d}{dx}\left[ x^2\right] }\)

Answer 9

keep in mind that \(\bf \cfrac{x^3}{3}-x^2\implies \cfrac{1}{3}\cdot x^3-x^2\)

and for that, allyou need, as already pointed out, the power rule