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

f(x)=e2xx3-24x3e5x+1

Short Answer

Expert verified

The derivative of function isy'=e2xx3-24x3e5x+12+12x2x3-2-1x-5e5x3e5x+1

Step by step solution

01

Step 1. Given Information

The given function isf(x)=e2xx3-24x3e5x+1

02

Step 2. Calculation    

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

lny=lne2xx3-24-lnx3e5x+1lny=lne2x+lnx3-24-lnx-ln3e5x+1lny=2x+4lnx3-2-lnx-ln3e5x+11yy'=2+4x3-23x2-1x-13e5x+15e5xy'=e2xx3-24x3e5x+12+12x2x3-2-1x-5e5x3e5x+1

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