If y = k, then y' = 0
The Derivative of a Constant is 0
If ƒ(x) = k for some constant k, then ƒ'(x) = 0
2. Power Rule
If y = x", then y' = nxn-1
If ƒ is a differentiable function, and if ƒ(x) = x", then ƒ'(x) = nxn-1 for any real number n
3. Exponential Rule:
If y = ex, then y' = ex
4. Logarithm Rule:
If y = 1n|x|, then y' = 1/x
5. Constant Times a Function Rule:
If y = kƒ, then y' = kf '
6. Sum Rule
If y = ƒ g, then y' = ƒ' g'
7. Product Rule
If y = ƒg, then y' = ƒg' ƒ' g
If ƒ and g are differentiable functions such that y = ƒ(x)g(x), then y' = ƒ(x)g' ƒ' (x)g(x)
8. Difference Rule
If y = ƒ - g, then y' = ƒ' - g'
9. Quotient Rule
To remember this formula: Simply remember that b comes before t in the alphabet Thus, the bottom function times the derivative of the top minus the top times the derivative of the bottom, all divided by the bottom squared!