Calculus Examples

$- \frac{x}{y}$

Step 1

Find the first derivative.

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Step 1.1

Since $- \frac{1}{y}$ is constant with respect to $x$ , the derivative of $- \frac{x}{y}$ with respect to $x$ is $- \frac{1}{y} \frac{d}{d x} [x]$ .

$- \frac{1}{y} \frac{d}{d x} [x]$

Step 1.2

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

$- \frac{1}{y} \cdot 1$

Step 1.3

Multiply $- 1$ by $1$ .

$f' (x) = - \frac{1}{y}$

Step 2

Since $- \frac{1}{y}$ is constant with respect to $x$ , the derivative of $- \frac{1}{y}$ 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 $0$ .

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