Title: CR_Diff_04
Course: Demonstrating STACK (v4.4.7)

The product rule for diﬀerentiation

Differentiate [value] with respect to [value].
Feedback: In order to solve this problem we will have to use the product rule calc_product_rule as follows: \[\begin{array}{rcl}\displaystyle \frac{d}{d[value]}[[value]] &\displaystyle =&\displaystyle \left[\frac{d}{d[value]}([value])\right]\cdot [value] + ([value])\cdot \left[\frac{d}{d[value]}[[value]]\right] \\ &\displaystyle =&\displaystyle ([value])\cdot [value] + ([value])\cdot [value] \\ &\displaystyle =&\displaystyle [value] \end{array}\]

Differentiate \[\left([value]\right)\left([value]\right)\] with respect to [value].
Feedback: In order to solve this problem we will have to use the product rule calc_product_rule as follows: \[\begin{array}{rcl}\displaystyle \frac{d}{d[value]}[[value]] &\displaystyle =&\displaystyle \left[\frac{d}{d[value]}([value])\right]\cdot [value] + ([value])\cdot \left[\frac{d}{d[value]}[[value]]\right] \\ &\displaystyle =&\displaystyle \left([value]\right)\cdot [value] + \left([value]\right)\cdot [value] \\ &\displaystyle =&\displaystyle [value] \end{array}\]

Find the following derivative: \[ \frac{d}{d[value]}[[value]]. \]
Feedback: In order to solve this problem we will have to use the product rule calc_product_rule as follows: \[\begin{array}{rcl}\displaystyle \frac{d}{d[value]}[[value]] &\displaystyle =&\displaystyle \left[\frac{d}{d[value]}[[value]]\right]\cdot [value] + [value]\cdot \left[\frac{d}{d[value]}[[value]]\right] \\ &\displaystyle =&\displaystyle [value]\cdot [value] + [value]\cdot [[value]] \\ &\displaystyle =&\displaystyle [value] \end{array}\]

Find the following derivative:
\[ \frac{d}{d[value]}[[value]]. \]
Feedback: In order to solve this problem we will have to use the product rule calc_product_rule as follows: \[\begin{array}{rcl}\displaystyle \frac{d}{d[value]}[[value]] &\displaystyle =&\displaystyle \left[\frac{d}{d[value]}[[value]]\right]\cdot [value] + [value]\cdot \left[\frac{d}{d[value]}[[value]]\right] \\ &\displaystyle =&\displaystyle [value]\cdot [value] + [value]\cdot [[value]] \\ &\displaystyle =&\displaystyle [value] \end{array}\]