**1. Constant Rule:**

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", theny' =nx^{n-1}

If ƒ is a differentiable function, and if ƒ( x) =x",then ƒ'(x) =nx^{n-1}for any real numbern

**3. Exponential Rule:**

If

y=e^{x}, theny' =e^{x}

**4. Logarithm Rule:**

If

y= 1n|x|, then y' = 1/x

**5. Constant Times a Function Rule:**

If

y=kƒ, theny'=kf '

**6. Sum Rule**

If y

=ƒg,theny'= ƒ'g'

**7. Product Rule**

If

y =ƒg,theny'= ƒg' ƒ' g

If ƒ and gare differentiable functions such thaty =ƒ(x)g(x), then y' =ƒ(x)g' ƒ'(x)g(x)

**8. Difference Rule**

If

y =ƒ -g,theny' =ƒ' -g'

**9. Quotient Rule**

To remember this formula: Simply remember that

bcomes beforetin the alphabet Thus, thebottom function times the derivative of the top minus the top times the derivative of the bottom, all divided by the bottom squared!

**10. Chain Rule:**

If

yis a differentiable function ofuanduis a differentiable function ofx and