What is the derivative of the polynomial f(x)=anxn+an−1xn−1+⋯+a1x+a0?

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Lesson Parent: 
Differentiation IV: Differentiation Formulas Everyone Must Know
Problem: 

What is the derivative of the polynomial f(x)=anxn+an−1xn−1+⋯+a1x+a0?

Answer: 

f′(x)=nanxn−1+(n−1)an−1xn−2+⋯+a1

SAMPLE SOLUTION

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Solution: 

Recall what a polynomial is here.

We know that <Sign in to see all the formulas> and that a0 is differentiable since it is a constant. Furthermore, if C is a constant and g(x) is differentiable then <Sign in to see all the formulas>. Therefore, each <Sign in to see all the formulas> is differentiable.

Since each term in <Sign in to see all the formulas> is differentiable, f′(x) is the sum of the derivatives of <Sign in to see all the formulas>. Therefore, <Sign in to see all the formulas>.