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Use logarithmic differentiation to find the derivatives of each of the functions in Exercises 49–58.

f(x)=12x1-x3x+1

Short Answer

Expert verified

The derivative of function isy'=12x1-x3x+11x-131-x+12(x+1

Step by step solution

01

Step 1. Given Information 

The given function isf(x)=12x1-x3x+1

02

Step 2. Calculation   

First, we will take the log on both sides and then differentiate it,

lny=ln12x1-x3x+1lny=ln(12x)+ln1-x3+lnx+1lny=ln(12x)+ln1-x13+ln(x+1)12lny=ln(12)+ln(x)+13ln(1-x)+12ln(x+1)1yy'=0+1x-13(1-x)+12(x+1)y'=12x1-x3x+11x-13(1-x)+12(x+1)

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