What is the derivative of f(x)=10/x^2+1?

1 Answer
Mar 12, 2018

f'(x)=-20x^-3

Explanation:

Start by rewriting the function like this:

f(x)=10x^-2+1

Now, the three derivative rules we will use are:

The Sum Rule

d/dx[f(x)+g(x)]=d/dx[f(x)]+d/dx[g(x)]

The Power Rule

d/dxx^n=nx^(n-1)

The Constant Rule

d/dx(k)=0

First, start with the Sum Rule:

f'(x)=d/dx(10x^-2)+d/dx(1)

Next, apply the Power Rule:

f'(x)=-2*10x^(-2-1)+d/dx(1)

Finally, apply the Constant Rule:

f'(x)=-2*10x^(-2-1)+0

Simplify:

f'(x)=-20x^-3