Find the derivative of the function f(x)=4x3−9x2+2x−1x
Simplify to find the derivative: f′(x)=10x2−272x+x−12x
Step 1 :First, rewrite the function as f(x)=4x52−9x32+2x12−x−12
Step 2 :Apply the power rule to find the derivative of each term: f′(x)=52⋅4x52−1−32⋅9x32−1+12⋅2x12−1+12⋅x−12−1
Step 3 :Simplify to find the derivative: f′(x)=10x2−272x+x−12x