Calculus Examples

$B (y) = c y^{- 3}$

Step 1

Since $c$ is constant with respect to $y$ , the derivative of $c y^{- 3}$ with respect to $y$ is $c \frac{d}{d y} [y^{- 3}]$ .

$c \frac{d}{d y} [y^{- 3}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d y} [y^{n}]$ is $n y^{n - 1}$ where $n = - 3$ .

$c (- 3 y^{- 4})$

Step 3

Simplify.

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Step 3.1

Reorder the factors of $c (- 3 y^{- 4})$ .

$- 3 c y^{- 4}$

Step 3.2

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

$- 3 c \frac{1}{y^{4}}$

Step 3.3

Multiply $- 3 c \frac{1}{y^{4}}$ .

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Step 3.3.1

Combine $- 3$ and $\frac{1}{y^{4}}$ .

$c \frac{- 3}{y^{4}}$

Step 3.3.2

Combine $c$ and $\frac{- 3}{y^{4}}$ .

$\frac{c \cdot - 3}{y^{4}}$

Step 3.4

Move $- 3$ to the left of $c$ .

$\frac{- 3 \cdot c}{y^{4}}$

Step 3.5

Move the negative in front of the fraction.

$- \frac{3 c}{y^{4}}$