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

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Answer 1 · 2018-03-12T03:21:40

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

Start by rewriting the function like this:

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

Now, the three derivative rules we will use are:

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

#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#