Calculus Examples

$A = \frac{1}{2} \cdot (b h)$

Step 1

Remove parentheses.

$A = \frac{1}{2} \cdot (b h)$

Step 2

Differentiate both sides of the equation.

$\frac{d}{d b} (A) = \frac{d}{d b} (\frac{1}{2} \cdot (b h))$

Step 3

The derivative of $A$ with respect to $b$ is $A'$ .

$A'$

Step 4

Differentiate the right side of the equation.

Tap for more steps...

Step 4.1

Combine fractions.

Tap for more steps...

Step 4.1.1

Combine $b$ and $\frac{1}{2}$ .

$\frac{d}{d b} [\frac{b}{2} \cdot h]$

Step 4.1.2

Combine $\frac{b}{2}$ and $h$ .

$\frac{d}{d b} [\frac{b h}{2}]$

Step 4.2

Since $\frac{h}{2}$ is constant with respect to $b$ , the derivative of $\frac{b h}{2}$ with respect to $b$ is $\frac{h}{2} \frac{d}{d b} [b]$ .

$\frac{h}{2} \frac{d}{d b} [b]$

Step 4.3

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

$\frac{h}{2} \cdot 1$

Step 4.4

Multiply $\frac{h}{2}$ by $1$ .

$\frac{h}{2}$

Step 5

Reform the equation by setting the left side equal to the right side.

$A' = \frac{h}{2}$

Step 6

Replace $A'$ with $\frac{d A}{d b}$ .

$\frac{d A}{d b} = \frac{h}{2}$