# What is the Power Rule?

##### 1 Answer

Sep 27, 2017

If we have

**Differentiation**

We *"multiply by the power and subtract one from the power"* :

Thus;

# dy/dx = d/dx (x^n) = nx^(n-1) #

**Integration**

We *"add one to the power, and divide by that new power"*

Thus:

# int \ y \ dx = int \ x^n \ dx = x^(n+1)/(n+1) + c #

**Examples:**

# d/dx( x^2 ) = 2x^(2-1) = 2x #

# d/dx( 3x^4 ) = 3(4)x^(4-1) = 12 x^3 #

# int \ x^2 \ dx = x^(2+1)/(2+1) + c = x^3/3 + c#

# int \ 3x^4 \ dx = 3x^(4+1)/(4+1) + c = 3/5x^5 + c#