Calculus Examples

$\frac{π}{a b}$

Step 1

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

$\frac{π}{b} \frac{d}{d a} [\frac{1}{a}]$

Step 2

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

$\frac{π}{b} \frac{d}{d a} [a^{- 1}]$

Step 3

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

$\frac{π}{b} (- a^{- 2})$

Step 4

Combine fractions.

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Step 4.1

Combine $\frac{π}{b}$ and $a^{- 2}$ .

$- \frac{π a^{- 2}}{b}$

Step 4.2

Move $a^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{π}{b a^{2}}$