Optimizing the Product Rule: Common Error Help for (5x-2)^3 / (2x+5)^4

In summary, The product rule error is a mathematical concept used in calculus to describe the error associated with estimating the product of two quantities. It is calculated by taking the absolute value of the sum of the individual errors divided by the product of the two quantities. Its significance lies in its ability to improve the accuracy and reliability of experimental data in scientific research. The product rule error cannot be negative and can be minimized by reducing individual errors and increasing precision in measurements.
  • #1
fr33pl4gu3
82
0
y = ( 5 x-2 ) 3 / ( 2 x+5 ) 4

I do it this way:

f(x) = (5x-2)3
g(x) = (2x+5)-4
f'(x) = 3(5x-2)2
g'(x) = -4(2x+5)-5

By using the product rule:

[3(5x-2)2](2x+5)-4 + (5x-2)3[-4(2x+5)-5]
3(5x-2)2(2x+5)-4 -4(2x+5)-5(5x-2)3

What's wrong with this answer?
 
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  • #2


Thread moved to Homework Help

f'(x) = 3(5x-2)2
g'(x) = -4(2x+5)-5

I do not believe you have differentiated correctly in these steps.
 
  • #3


Is it this way??

f'(x) = 15(5x-2)2
g'(x) = -8(2x+5)-5
 
Last edited:
  • #4


Yes, got it. Thanks for pointing out the error.
 

What is the product rule error?

The product rule error is a mathematical concept used in calculus that describes the error associated with estimating the product of two quantities using their individual estimates. It is commonly used in situations where the two quantities are dependent on each other.

How is the product rule error calculated?

The product rule error can be calculated by taking the absolute value of the sum of the individual errors divided by the product of the two quantities being multiplied. This can be represented by the formula: |Δxy/xy|.

What is the significance of the product rule error in scientific research?

The product rule error is crucial in scientific research as it allows for more accurate estimation of values and helps to determine the reliability of experimental data. It also helps scientists to identify and correct any sources of error in their experiments.

Can the product rule error be negative?

No, the product rule error cannot be negative. This is because it is a measure of the absolute value of the error and is always expressed as a positive value.

How can the product rule error be minimized?

The product rule error can be minimized by reducing the individual errors of the quantities being multiplied and by increasing the precision of the measurement devices used. It is also important to use appropriate rounding techniques and to take repeated measurements to improve accuracy.

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