• Constant function rule: \(f(x) = k ; f'(x) = 0\)
• Linear function rule: \(f(x) = mx + b ; f'(x) = m\)
• Power function rule: \(f(x) = kx^n ; f'(x) = nkx^{n-1}\)
• Sums and differences rule: \(f(x) = g(x) \pm h(x) ; f'(x) = g'(x) \pm h'(x)\)
• Product rule: \(f(x) = g(x) \cdot h(x) ; f'(x) = g(x) \cdot h'(x) + h(x) \cdot g'(x)\)
• Quotient rule: \(f(x) = \frac{g(x)}{h(x)} ; f'(x) = \frac{h(x) \cdot g'(x) - g(x) \cdot h'(x)}{h(x)^2}\)
• Generalized power rule: \(f(x) = [g(d)]^n ; f'(x) = n[g(x)]^{n-1} \cdot g'(x)\)
• Chain rule: \(y=f\left(g(x)\right);\frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}\)
• Natural exponential function rule: \(f(x) = e^{g(x)} ; f'(x) = e^{g(x)} \cdot g'(x)\)
• Natural log function rule: \(f(x)=\ln\left(g(x)\right);f'(x)=\frac{g'(x)}{g(x)}\)
• Partial Product Rule (others similar): \(z = g(x, y) \cdot h(x, y) ; \frac{\partial z}{\partial x} = g(x, y) \cdot \frac{\partial h}{\partial x} + h(x, y) \cdot \frac{\partial g}{\partial x}\)