Calculus Examples

$v (p) = \frac{n R t}{p}$

Step 1

Since $n R t$ is constant with respect to $p$ , the derivative of $\frac{n R t}{p}$ with respect to $p$ is $n R t \frac{d}{d p} [\frac{1}{p}]$ .

$n R t \frac{d}{d p} [\frac{1}{p}]$

Step 2

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

$n R t \frac{d}{d p} [p^{- 1}]$

Step 3

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

$n R t (- p^{- 2})$

Step 4

Simplify.

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Step 4.1

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

$n R t (- \frac{1}{p^{2}})$

Step 4.2

Combine terms.

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Step 4.2.1

Combine $n$ and $\frac{1}{p^{2}}$ .

$R t (- \frac{n}{p^{2}})$

Step 4.2.2

Combine $R$ and $\frac{n}{p^{2}}$ .

$t (- \frac{R n}{p^{2}})$

Step 4.2.3

Combine $t$ and $\frac{R n}{p^{2}}$ .

$- \frac{t R n}{p^{2}}$