Calculus Examples

$y = \sqrt{2^{2} + 21}$

Step 1

Find the first derivative.

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Step 1.1

Raise $2$ to the power of $2$ .

$\frac{d}{d x} [\sqrt{4 + 21}]$

Step 1.2

Add $4$ and $21$ .

$\frac{d}{d x} [\sqrt{25}]$

Step 1.3

Rewrite $25$ as $5^{2}$ .

$\frac{d}{d x} [\sqrt{5^{2}}]$

Step 1.4

Pull terms out from under the radical, assuming positive real numbers.

$\frac{d}{d x} [5]$

Step 1.5

Since $5$ is constant with respect to $x$ , the derivative of $5$ 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 $0$ .

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