Calculus Examples

$y = \frac{π}{x}$

Step 1

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

$π \frac{d}{d x} [\frac{1}{x}]$

Step 2

Rewrite $\frac{1}{x}$ as $x^{- 1}$ .

$π \frac{d}{d x} [x^{- 1}]$

Step 3

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

$π (- x^{- 2})$

Step 4

Simplify.

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Step 4.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$π (- \frac{1}{x^{2}})$

Step 4.2

Combine $π$ and $\frac{1}{x^{2}}$ .

$- \frac{π}{x^{2}}$