Calculus Examples

$C x (1 - e^{- k x})$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

Since $x (1 - e^{- k x})$ is constant with respect to $C$ , the derivative of $C x (1 - e^{- k x})$ with respect to $C$ is $x (1 - e^{- k x}) \frac{d}{d C} [C]$ .

$x (1 - e^{- k x}) \frac{d}{d C} [C]$

Step 3

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

$x (1 - e^{- k x}) \cdot 1$

Step 4

Multiply $x$ by $1$ .

$x (1 - e^{- k x})$

Step 5

Simplify.

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Step 5.1

Apply the distributive property.

$x \cdot 1 + x (- e^{- k x})$

Step 5.2

Multiply $x$ by $1$ .

$x + x (- e^{- k x})$

Step 5.3

Reorder terms.

$- e^{- k x} x + x$

Step 5.4

Reorder factors in $- e^{- k x} x + x$ .

$- x e^{- k x} + x$