Calculus Examples

$f (x) = D \cdot (m \cdot \log (\frac{x \cdot (B - A \cdot C)}{c}) - x \cdot A + b)$

Step 1

Multiply $- x$ by $A$ .

$\frac{d}{d D} [D \cdot (m \log (\frac{x (B - A C)}{c}) - x A + b)]$

Step 2

Since $m \log (\frac{x (B - A C)}{c}) - x A + b$ is constant with respect to $D$ , the derivative of $D (m \log (\frac{x (B - A C)}{c}) - x A + b)$ with respect to $D$ is $(m \log (\frac{x (B - A C)}{c}) - x A + b) \frac{d}{d D} [D]$ .

$(m \log (\frac{x (B - A C)}{c}) - x A + b) \frac{d}{d D} [D]$

Step 3

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

$(m \log (\frac{x (B - A C)}{c}) - x A + b) \cdot 1$

Step 4

Multiply $m \log (\frac{x (B - A C)}{c}) - x A + b$ by $1$ .

$m \log (\frac{x (B - A C)}{c}) - x A + b$

Step 5

Simplify.

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Step 5.1

Apply the distributive property.

$m \log (\frac{x B + x (- A C)}{c}) - x A + b$

Step 5.2

Reorder terms.

$b + m \log (\frac{x B + x (- A C)}{c}) - A x$

Step 5.3

Factor $x$ out of $x B + x (- A C)$ .

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Step 5.3.1

Factor $x$ out of $x B$ .

$b + m \log (\frac{x (B) + x (- A C)}{c}) - A x$

Step 5.3.2

Factor $x$ out of $x (B) + x (- A C)$ .

$b + m \log (\frac{x (B - A C)}{c}) - A x$