Calculus Examples

$f (x) = \sqrt{r} + \sqrt[3]{r}$

Step 1

Find the first derivative.

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Step 1.1

By the Sum Rule, the derivative of $\sqrt{r} + \sqrt[3]{r}$ with respect to $x$ is $\frac{d}{d x} [\sqrt{r}] + \frac{d}{d x} [\sqrt[3]{r}]$ .

$\frac{d}{d x} [\sqrt{r}] + \frac{d}{d x} [\sqrt[3]{r}]$

Step 1.2

Since $\sqrt{r}$ is constant with respect to $x$ , the derivative of $\sqrt{r}$ with respect to $x$ is $0$ .

$0 + \frac{d}{d x} [\sqrt[3]{r}]$

Step 1.3

Since $\sqrt[3]{r}$ is constant with respect to $x$ , the derivative of $\sqrt[3]{r}$ with respect to $x$ is $0$ .

$0 + 0$

Step 1.4

Add $0$ and $0$ .

$f' (x) = 0$

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

The second derivative of $f (x)$ with respect to $x$ is $0$ .

$0$