How do you find f’(x) if f(x)= (x+1)^101

Answer 1

Okay so this problem will utilize the power rule and the chain rule.

The chain rule is something that you can use when there's a function inside of another function. In this case the function (x+1) is inside the function (x+1)^101.

Basically all you have to do is take the derivative of the outside function, while leaving the inside alone, and then multiply it by the derivative of the inside.

The power rule makes taking the derivative of something raised to some power really easy. Basically you multiply the base by the exponent, and then lower the exponent by 1. For example, the derivative of x^5 will equal 5x^4.

In this case you take 101 and move it to the front, while lowering 101 by 1. This turns out to

101(x+1)^100

You then multiply this by the derivative of the inside function (x+1). The derivative of (x+1) is just 1, so the final answer is still 101(x+1)^100

Answer 2

Use the Power Rule. (uⁿ)' = nu^n-1u'

So, If f(x) = (x+1)¹⁰¹, then f'(x) = 101(x+1)¹⁰⁰(x+1)' = 101(x+1)¹⁰⁰