Take the derivative respect to U

  • Thread starter afcwestwarrior
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In summary, the derivative of V with respect to u is equal to -(1/2) * u^(-3/2). The original equation can be rewritten as V= T^(1/2)*u^(-1/2), which is in the form of y=c*x^n. The generic formula for this form is y=c*x^n, where c is the constant. The final answer, including the constant, is V= T^(1/2)*-(1/2) * u^(-3/2).
  • #1
afcwestwarrior
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V = [tex]\sqrt{T/u}[/tex]

Take the derivative respect to U. I'm having trouble with this.

[tex]\sqrt{T}[/tex] * 1/[tex]\sqrt{u}[/tex]


So would u look like this U^-(1/2)

since T is constant I'd leave it alone.

it would become -(1/2) * u^(-3/2)


Am I right or Am I wrong.
 
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  • #2


Right now you can re-write the equation as V= T^(1/2)*u^(-1/2)
effectively this is in the form of y=c*x^n (just to go back to familiar notation)
what is the generic formula for this? Your close, but your leaving out the constant...

So what would the answer be once you include it?
 
  • #3


V= T^(1/2)*-(1/2) * u^(-3/2)
 
  • #4


looks pretty good to me!
 
  • #5


since T is a constant your answer is right
 
  • #6


Thanks for the assistance!
 

What does it mean to "take the derivative respect to U"?

When we say "take the derivative respect to U," we are referring to finding the rate of change of a function with respect to the variable U. This means finding how much the output of the function changes for every unit change in U.

Why do we need to take the derivative respect to U?

Taking the derivative respect to U allows us to understand the relationship between the input variable U and the output of a function. It is especially useful in determining the maximum and minimum values of a function, as well as the slope of a curve at a specific point.

How do you take the derivative respect to U?

To take the derivative respect to U, we use the rules of differentiation, such as the power rule, product rule, and chain rule. We first rewrite the function in terms of U, then differentiate each term with respect to U, keeping in mind the rules of differentiation.

What is the difference between partial derivative and derivative respect to U?

A partial derivative is when we take the derivative of a function with respect to one variable while holding all other variables constant. On the other hand, taking the derivative respect to U means finding the rate of change of a function with respect to the specific variable U, while holding all other variables constant.

Can we take the derivative respect to U for any type of function?

Yes, we can take the derivative respect to U for any type of function, including polynomial, exponential, logarithmic, and trigonometric functions. The rules of differentiation apply to all types of functions, making it possible to find the derivative respect to U for any given function.

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