Derivative of $$$\pi \left(z - 1\right)$$$ with respect to $$$\pi$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{d\pi} \left(\pi \left(z - 1\right)\right)$$$.
Solution
Apply the constant multiple rule $$$\frac{d}{d\pi} \left(c f{\left(\pi \right)}\right) = c \frac{d}{d\pi} \left(f{\left(\pi \right)}\right)$$$ with $$$c = z - 1$$$ and $$$f{\left(\pi \right)} = \pi$$$:
$${\color{red}\left(\frac{d}{d\pi} \left(\pi \left(z - 1\right)\right)\right)} = {\color{red}\left(\left(z - 1\right) \frac{d}{d\pi} \left(\pi\right)\right)}$$Apply the power rule $$$\frac{d}{d\pi} \left(\pi^{n}\right) = n \pi^{n - 1}$$$ with $$$n = 1$$$, in other words, $$$\frac{d}{d\pi} \left(\pi\right) = 1$$$:
$$\left(z - 1\right) {\color{red}\left(\frac{d}{d\pi} \left(\pi\right)\right)} = \left(z - 1\right) {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{d\pi} \left(\pi \left(z - 1\right)\right) = z - 1$$$.
Answer
$$$\frac{d}{d\pi} \left(\pi \left(z - 1\right)\right) = z - 1$$$A