Question

Find the derivative of the given function. x^5/3-x^-1/3.....


** answer is 5x^2+1 divided by 3x^4/3

Answer 1

Yeah, use the power rule, I guess. Bring down the exponents, subtract one to get new powers, etc.

Answer 2

\[\frac{x^5}{3}-\frac{x^{-1}}{3} ?\]

Answer 3

\[x ^{5/3}-x ^{-1/3}\]

Answer 4

do you remember \[(x^n)'=nx^{n-1}\]

Answer 5

\[(x^\frac{5}{3})'=\frac{5}{3}x^{\frac{5}{3}-1}\]

Answer 6

\[(x^\frac{-1}{3})'=\frac{-1}{3}x^{\frac{-1}{3}-1}\]

Answer 7

I don't remember what it's called, but you need to know the addition rule too. The one that says the derivative of a plus b is equal to the derivative of a plus the derivative of b.

Answer 8

\[\frac{5}{3}x^\frac{2}{3}-\frac{-1}{3}x^\frac{-4}{3}\]

Answer 9

now you can use algebra to write what they have

Answer 10

\[\frac{5x^\frac{2}{3}}{3}+\frac{1}{3x^\frac{4}{3}}=\frac{5x^\frac{2}{3}x^\frac{4}{3}+1}{3x^\frac{4}{3}}\]

Answer 11

\[=\frac{5x^\frac{6}{3}+1}{3x^\frac{4}{3}}=\frac{5x^2+1}{3x^\frac{4}{3}}\]

Answer 12

thank you