Calculus Examples

$f (X) = (x^{2} - 1) (\frac{2}{3} x^{3} + 5 x + 1)$

Step 1

Find the first derivative.

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Step 1.1

Combine $\frac{2}{3}$ and $x^{3}$ .

$\frac{d}{d X} [(x^{2} - 1) (\frac{2 x^{3}}{3} + 5 x + 1)]$

Step 1.2

Since $(x^{2} - 1) (\frac{2 x^{3}}{3} + 5 x + 1)$ is constant with respect to $X$ , the derivative of $(x^{2} - 1) (\frac{2 x^{3}}{3} + 5 x + 1)$ with respect to $X$ is $0$ .

$f' (X) = 0$

Step 2

Since $0$ is constant with respect to $X$ , the derivative of $0$ with respect to $X$ is $0$ .

$f'' (X) = 0$

Step 3

Since $0$ is constant with respect to $X$ , the derivative of $0$ with respect to $X$ is $0$ .

$f''' (X) = 0$

Step 4

Since $0$ is constant with respect to $X$ , the derivative of $0$ with respect to $X$ is $0$ .

$f^{4} (X) = 0$

Step 5

The fourth derivative of $f (X)$ with respect to $X$ is $0$ .

$0$