Which of the following is not a valid differentiation rule, a. \( \frac{d}{d x}(c)=0, c \) is a constant. ( b. None of these options. o c. \( \frac{d}{d x}\left(\frac{f}{g}\right)=\frac{f^{\prime} g+f g^{\prime}}{g^{2}}, g \neq 0 \). d. \( \frac{d}{d x}(f \pm g)=f^{\prime} \pm g^{\prime} \). e. \( \frac{d}{d x}(f g)=f^{\prime} g+f g^{\prime} \).

To determine which of the given options is not a valid differentiation rule, let's analyze each option: a. \( \frac{d}{d x}(c)=0, c \) is a constant. This is a valid differentiation rule. The derivative of a constant is always 0. b. None of these options. This option does not provide any differentiation rule. c. \( \frac{d}{d x}\left(\frac{f}{g}\right)=\frac{f^{\prime} g+f g^{\prime}}{g^{2}}, g \neq 0 \). This is a valid differentiation rule. It is the quotient rule for differentiation. d. \( \frac{d}{d x}(f \pm g)=f^{\prime} \pm g^{\prime} \). This is a valid differentiation rule. It is the sum/difference rule for differentiation. e. \( \frac{d}{d x}(f g)=f^{\prime} g+f g^{\prime} \). This is a valid differentiation rule. It is the product rule for differentiation. Therefore, the option that is not a valid differentiation rule is option b. None of these options.