Since mathematicians are generally pretty lazy, we like to come up with shortcuts to complex formulas. The power rule simplifies the derivative for one of the most common functions in this course: polynomials.
Let’s imagine you want to take the derivative of x^n
According to the Binomial Theorem (this is the formula you use when calculating (a+b)^2=a^2+2ab+b^2 ),
Thus, d/dx x^n = nx^n-1
Don’t worry -- you won’t have to understand this proof for the exam. But, if you’re a nerd like me, it can be helpful to know where it comes from. 🤓
The Power Rule ✊
For any differentiable function f(x),
d/dx x^n = nx^(n-1)
For the most part, you’ll take derivatives using the power rule.
Example: Find the derivative of f(x)= x^7
f'(x)= 7x^(7-1) = 7x^6
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