Calculus Examples

$C' (x) = x^{- \frac{2}{3}}$

Step 1

The function $C (x)$ can be found by evaluating the indefinite integral of the derivative $C' (x)$ .

$C (x) = \int C' (x) d x$

Step 2

By the Power Rule, the integral of $x^{- \frac{2}{3}}$ with respect to $x$ is $3 x^{\frac{1}{3}}$ .

$3 x^{\frac{1}{3}} + C$

Step 3

The function $C$ if derived from the integral of the derivative of the function. This is valid by the fundamental theorem of calculus.

$C (x) = 3 x^{\frac{1}{3}} + C$