Calculus Examples

$\frac{x}{y}$

Step 1

Find the 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 $\frac{1}{y}$ by $1$ .

$\frac{1}{y}$

Step 2

Set the derivative equal to $0$ then solve the equation $\frac{1}{y} = 0$ .

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Step 2.1

Set the numerator equal to zero.

$1 = 0$

Step 2.2

Since $1 \neq 0$ , there are no solutions.

No solution

Step 3

There are no solution found by setting the derivative equal to $0$ , $\frac{1}{y} = 0$ so there are no horizontal tangent lines.

No horizontal tangent lines found

Step 4