Simple differentiation for YOU PPL

In summary, the conversation is about differentiating the function y = 4x^(2x) and a step-by-step explanation is given. The key steps include defining a new function z and applying log to both sides, using the chain and product rule, and multiplying the final answer by 4. The conversation also mentions that this topic may be better suited for the homework help or calculus forum.
  • #1
beanryu
92
0
how do I differentiate 4*x^(2x)?
The professor explained to the class while i was sleeping...
and I don't quite get what my fd was talking about...

can anyone help?
I know x^(2x) is different from a constant to (2x)
but I don't no how to do it...

is the answer (x^x)(lnx)+(x^x)
if so could you guys explain it step by step? THANX!
 
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  • #2
Call it a function, y:
y = 4x^(2x)
There's one easy way to do it that I can think of...
First thing we do, let's ignore the 4... it'll probably end up confusing you; what we'll do with the final answer is multiply it before, so let's define a new function z:
z = x^(2x)
Apply log to both sides...
log z = 2x log x
Use the chain and product rule..
z'/z = 2log x + 2
z' = (x^2x)(2log x + 2)
Now, times the whole thing by 4...
y' = (4x^2x)(2log x + 2)

By the way I think this should be in the homework help forum or the calculus forum..
 
  • #3
Thank You!

You Are My Savior!

Thanks Alot!

I Love You!
 

1. What is simple differentiation?

Simple differentiation is a mathematical process used to find the rate of change of a function at a specific point. It involves finding the derivative of a function, which represents the slope of the tangent line at that point.

2. Why is differentiation important?

Differentiation is important because it allows us to analyze and understand the behavior of a function. It is used in many fields, including physics, engineering, economics, and statistics, to model and solve real-world problems.

3. What are the basic rules of differentiation?

The basic rules of differentiation include the power rule, product rule, quotient rule, and chain rule. The power rule states that the derivative of x^n is nx^(n-1), while the product rule states that the derivative of f(x)g(x) is f'(x)g(x) + f(x)g'(x). The quotient rule and chain rule are used for more complex functions.

4. How is differentiation related to integration?

Differentiation and integration are inverse operations, meaning that they undo each other. The derivative of a function is the slope of its tangent line, while the integral of a function is the area under its curve. Integration can be thought of as the reverse process of differentiation.

5. Are there any common mistakes to watch out for in differentiation?

Yes, there are a few common mistakes that can be made in differentiation. These include forgetting to apply the chain rule, mixing up the order of terms in the product rule, and not simplifying expressions before taking the derivative. It is important to double check your work and be aware of these potential errors.

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