Understanding the Derivative of y = 2x sqrt(x^2 + 1)

In summary, the conversation discusses how to differentiate the function y=2x square root of (x^2+1) using the chain rule, power rule, and product rule. It also explains the steps to apply these rules and clarifies any confusion about their application.
  • #1
lotus_daemon
4
0
y = 2x square root of (x^2+1)

I'm not exactly sure how to start off this problem. Am I supposed to use the chain rule or some other rule? I really need help on understanding this, so if anyone is kind enough to provide detailed steps, I thank you so much.
 
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  • #2
What other rules do you know for differentiating a function (power rule, product rule, quotient rule, etc) that would apply here?
 
  • #3
VeeEight said:
What other rules do you know for differentiating a function (power rule, product rule, quotient rule, etc) that would apply here?

It looks like I would use the chain rule for this, but I don't know "how" to start it out. =(
 
  • #4
There are powers and products of terms in the function, so why wouldn't you use the power rule and product rule? Do you know what they are and how to use them? How do they apply to this function?
 
  • #5
VeeEight said:
There are powers and products of terms in the function, so why wouldn't you use the power rule and product rule? Do you know what they are and how to use them? How do they apply to this function?

I know what they are but I didn't think that I could apply them in this particular problem. If it's possible, can you please show me how? =( I'm used to the chain rule...
 
  • #6
Why did you think that they don't apply for this problem?

You have the function written as y= 2x sqrt(x^2 + 1)
which is the same as y=2x (x^2 + 1)^(1/2)
So let 2x be some function, call it g(x) and (x^2 + 1)^(1/2) be another function, call it h(x).

You can write y as the product of two functions, y=h(x)g(x). So you can apply the product rule here. Remember to apply the power rule and chain rule when you differentiate h(x)
 
  • #7
VeeEight said:
Why did you think that they don't apply for this problem?

You have the function written as y= 2x sqrt(x^2 + 1)
which is the same as y=2x (x^2 + 1)^(1/2)
So let 2x be some function, call it g(x) and (x^2 + 1)^(1/2) be another function, call it h(x).

You can write y as the product of two functions, y=h(x)g(x). So you can apply the product rule here. Remember to apply the power rule and chain rule when you differentiate h(x)

Hmmm...okay. I get it now. Thank you for your help. =)
 

1. What is the formula for Y = 2x square root of (x^2+1)?

The formula for Y = 2x square root of (x^2+1) is a mathematical expression that represents a relationship between the variables x and y. It is often used in algebra and calculus to solve for the value of y given a specific value for x.

2. How do you graph Y = 2x square root of (x^2+1)?

To graph Y = 2x square root of (x^2+1), you can plot points on a coordinate plane by choosing different values for x and solving for the corresponding values of y using the formula. Once you have several points, you can connect them with a smooth curve to create the graph.

3. What is the domain of Y = 2x square root of (x^2+1)?

The domain of Y = 2x square root of (x^2+1) is all real numbers except for x = 0. This is because the expression x^2+1 cannot be equal to 0, so the square root would be undefined. In other words, the domain is all values of x that make the expression under the square root non-negative.

4. What is the range of Y = 2x square root of (x^2+1)?

The range of Y = 2x square root of (x^2+1) is all real numbers greater than or equal to 0. This is because the square root of any number is always positive or 0, and multiplying by 2x does not change this. Therefore, the range includes all possible values of y for any given value of x.

5. How is Y = 2x square root of (x^2+1) used in science?

Y = 2x square root of (x^2+1) can be used in various scientific applications, such as physics, engineering, and biology. It can be used to model relationships between different variables and make predictions based on experimental data. In physics, it can be used to calculate velocity and acceleration, while in biology it can be used to model population growth. It is a versatile formula that is used in many different scientific fields.

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