Calculus Examples

$b (y) = c y^{- 6}$

Step 1

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

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

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d y} [y^{n}]$ is $n y^{n - 1}$ where $n = - 6$ .

$c (- 6 y^{- 7})$

Step 3

Simplify.

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Step 3.1

Reorder the factors of $c (- 6 y^{- 7})$ .

$- 6 c y^{- 7}$

Step 3.2

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

$- 6 c \frac{1}{y^{7}}$

Step 3.3

Multiply $- 6 c \frac{1}{y^{7}}$ .

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Step 3.3.1

Combine $- 6$ and $\frac{1}{y^{7}}$ .

$c \frac{- 6}{y^{7}}$

Step 3.3.2

Combine $c$ and $\frac{- 6}{y^{7}}$ .

$\frac{c \cdot - 6}{y^{7}}$

Step 3.4

Move $- 6$ to the left of $c$ .

$\frac{- 6 \cdot c}{y^{7}}$

Step 3.5

Move the negative in front of the fraction.

$- \frac{6 c}{y^{7}}$