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Simple Differentials - please help?

  • Thread starter Nachore
  • Start date
  • #1
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1. The problem
Use Differentials to approximate (24.5)^(1/2) + (9.5)^(1/2). Compare your answer to your calculator's answer.

Homework Equations



I used z = (x)^(1/2) + (y)^(1/2)

The Attempt at a Solution



What I used:
let z = (x)^(1/2) + (y)^(1/2)
x = 25
y = 10
dx = 0.5
dy = 0.5
Using http://www.maths.soton.ac.uk/~jav/soton/ma155/lectures2/img203.gif [Broken].[/URL]
I plugged in 1/(2(x)^(1/2)) for the partial derivative w/respect to x, and 1/(2(y)^(1/2)) for the partial derivative w/respect to y. When I plug into the formula, I get 0.1290 not 8.0139 like in the calculator. What am I doing wrong?
 
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Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
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1. The problem
Use Differentials to approximate (24.5)^(1/2) + (9.5)^(1/2). Compare your answer to your calculator's answer.

Homework Equations



I used z = (x)^(1/2) + (y)^(1/2)

The Attempt at a Solution



What I used:
let z = (x)^(1/2) + (y)^(1/2)
x = 25
y = 10
dx = 0.5
dy = 0.5
Using http://www.maths.soton.ac.uk/~jav/soton/ma155/lectures2/img203.gif [Broken].[/URL]
I plugged in 1/(2(x)^(1/2)) for the partial derivative w/respect to x, and 1/(2(y)^(1/2)) for the partial derivative w/respect to y. When I plug into the formula, I get 0.1290 not 8.0139 like in the calculator. What am I doing wrong?
You the did the derivative wrong. The derivative of xn is n xn-1, not n xn as you have.
 
Last edited by a moderator:

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