Question

If f(x) = x^-(1/3) find the derivative of f(x)

Answer 1

\[dx^{n}/dx=nx^{n-1}\]
unless n=-1

Answer 2

therefore
\[dx^{-1/3}/dx=-1/3x^{-4/3}\]

Answer 3

Or
\[f(x) = x^{-1/3}=1/\sqrt[3]{x}\]
\[f^{\prime}(x) =-1/3 \times x^{-4/3} = -1/(3x \sqrt[3]{x})\]

Answer 4

wait is teh second way teh same asnwer as teh first?

Answer 5

yes

Answer 6

your looking for the \(lim_{h->0}\cfrac{f(x+h)-f(x)}{h}\) version tho right?

Answer 7

yeah

Answer 8

wait its ok....will will give u the same asnwer cuz the limh-> 0 is longer

Answer 9

right

Answer 10

i mean it wanst bad