Calculus Examples

$x y$

Step 1

Find the first derivative.

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Step 1.1

Since $y$ is constant with respect to $x$ , the derivative of $x y$ with respect to $x$ is $y \frac{d}{d x} [x]$ .

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

Step 1.2

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$y \cdot 1$

Step 1.3

Multiply $y$ by $1$ .

$f' (x) = y$

Step 2

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

$f'' (x) = 0$