Calculus Examples

$c y^{- 6}$

Step 1

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

$\frac{d}{d c} [c \frac{1}{y^{6}}]$

Step 2

Combine $c$ and $\frac{1}{y^{6}}$ .

$\frac{d}{d c} [\frac{c}{y^{6}}]$

Step 3

Since $\frac{1}{y^{6}}$ is constant with respect to $c$ , the derivative of $\frac{c}{y^{6}}$ with respect to $c$ is $\frac{1}{y^{6}} \frac{d}{d c} [c]$ .

$\frac{1}{y^{6}} \frac{d}{d c} [c]$

Step 4

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

$\frac{1}{y^{6}} \cdot 1$

Step 5

Multiply $\frac{1}{y^{6}}$ by $1$ .

$\frac{1}{y^{6}}$