Deriving a Complex Function: What is the Best Method?

  • Thread starter Spectre32
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In summary, the conversation discusses the process of deriving a function, specifically 1/(5x^7sqrt(x)). The speaker suggests using the quotient rule and asks if there are any programs available to help with derivatives and integration. Another speaker clarifies the function and gives a different approach using the power rule and taking the logarithm. The conversation ends with the speaker thanking for the help.
  • #1
Spectre32
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Ok i have an easy function:

1/(5x^7sqrt(x)) Now i am asked to derive this. What would be the best method. I thought about the quotent rule, and I'm thinkin that's my best bet. Also, does anyone know if there is a program out there that shows steps to Derivaties and Intergration. I have my final comming up and i want to know if I'm doing all of my review problems correctly.
 
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  • #2
Do you mean

[tex]\frac{1}{5x^7\sqrt{x}}[/tex]

If so, this can be written as

[tex]\frac{1}{5}x^{-15/2}[/tex]

and differentiated using the power rule.

cookiemonster
 
  • #3
ahhh whoops, i forgot about that, Thanks for the help.
 
  • #4
Your description of the function is not clear. Is the sqrt(x) also in the exponent ?

If you mean y = 1/[5*x^{7*sqrt(x)}], it's a little harder. Then you take the logarithm on both sides - which converts the exponent into a product - before differentiating.

That way, the answer would be y' = [-7/{sqrt(x)*x^(7*sqrt(x))}]*[1 - (1/2)*log(x)]
 

1. What is "Dy/Dx" in calculus?

"Dy/Dx" is a notation used in calculus to represent the derivative of a function. It represents the instantaneous rate of change of a function with respect to its independent variable.

2. How do you calculate "Dy/Dx"?

To calculate "Dy/Dx", you can use the power rule, product rule, quotient rule, or chain rule depending on the specific function. These rules involve taking the derivative of each term in the function and combining them using algebraic operations.

3. What is the significance of "Dy/Dx" in calculus?

"Dy/Dx" is significant in calculus because it allows us to analyze the behavior of a function at a specific point. It helps us understand the rate of change of a function and its slope at a given point, which is crucial in many applications of calculus.

4. How is "Dy/Dx" related to the slope of a curve?

"Dy/Dx" is directly related to the slope of a curve. In fact, "Dy/Dx" is the mathematical representation of the slope of a curve at a particular point. It tells us how quickly the function is changing at that point and in which direction.

5. Can "Dy/Dx" be negative?

Yes, "Dy/Dx" can be negative. A negative value for "Dy/Dx" indicates that the function is decreasing at that point, while a positive value indicates that the function is increasing. A value of zero for "Dy/Dx" means that the function is neither increasing nor decreasing at that point.

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