Answer
a) Power Rule: $\frac{d}{dx}x^{n} = nx^{n-1}$
b) The Constant Multiple Rule: $\frac{d}{dx}(c \times f(x)) = c\frac{d}{dx}(f(x)) $
c) Sum Rule: $\frac{d}{dx}(f(x) + g(x)) = \frac{d}{dx}(f(x)) + \frac{d}{dx}(g(x))$
d) Difference Rule: $\frac{d}{dx}(f(x) - g(x)) = \frac{d}{dx}(f(x)) - \frac{d}{dx}(g(x))$
e) Product Rule: $\frac{d}{dx}(f(x) \times g(x)) = \frac{d}{dx}(f(x))\times g(x) + \frac{d}{dx}(g(x))\times f(x)$
f) Quotient Rule: $\frac{d}{dx}(\frac {f(x)}{g(x)}) = \frac{\frac{d}{dx}(f(x))\times g(x) - \frac{d}{dx}(g(x))\times f(x)}{(g(x))^{2}}$
g) Chain Rule: $\frac{d}{dx}(f(g(x))) = f'(g(x))\times g'(x)$
Work Step by Step
a) Power Rule: $\frac{d}{dx}x^{n} = nx^{n-1}$
b) The Constant Multiple Rule: $\frac{d}{dx}(c \times f(x)) = c\frac{d}{dx}(f(x)) $
c) Sum Rule: $\frac{d}{dx}(f(x) + g(x)) = \frac{d}{dx}(f(x)) + \frac{d}{dx}(g(x))$
d) Difference Rule: $\frac{d}{dx}(f(x) - g(x)) = \frac{d}{dx}(f(x)) - \frac{d}{dx}(g(x))$
e) Product Rule: $\frac{d}{dx}(f(x) \times g(x)) = \frac{d}{dx}(f(x))\times g(x) + \frac{d}{dx}(g(x))\times f(x)$
f) Quotient Rule: $\frac{d}{dx}(\frac {f(x)}{g(x)}) = \frac{\frac{d}{dx}(f(x))\times g(x) - \frac{d}{dx}(g(x))\times f(x)}{(g(x))^{2}}$
g) Chain Rule: $\frac{d}{dx}(f(g(x))) = f'(g(x))\times g'(x)$
