Question

find the derivative of the following:
3x^2 ln(2x)

e^2x ln√x+3

please try and show few steps and laws of logarithmics.

Answer 1

Hi sasha,

Let me explain the methods step by step :

a)3x^2 ln(2x)
For this question, product rule must be applied : uv = udv/dx + vdu/dx
where u = 3x^2 & v = ln(2x)

Differentiate u, du/dx = 6x(I'm sure you know the basic differentiation)

Differentiate v ,dv/dx = 2/2x = 1/x

uv = (3x^2)(1/x) +(ln(2x)(6x))
= 3x + 6x ln(2x)

This answer can be simplified further to:
3x(1+2ln(2x)),using distributive law equation

Try to apply the similar concept for b).

Differentiation & integration are indeed easy if you understand the concepts. Try to download the differentiation & integration formula sheet from internet for your own good & keep practicing! Good luck :)!