Simple partial differentiation

Thread starter kasse
Start date May 17, 2008
Tags

Differentiation Partial Partial differentiation

Click For Summary

The discussion focuses on differentiating the function f = arctan(u/v) with respect to u using the chain rule. The initial attempt yielded fu = 1/(v + u^2/v), which differs from the solutions manual's answer of v/(u^2 + v^2). Participants suggest multiplying the numerator and denominator by "v" to reconcile the two results. This indicates a common approach to simplifying expressions in calculus. The conversation highlights the importance of careful manipulation of fractions in differentiation.

May 17, 2008

kasse

Homework Statement

Differentiate f = arctan(u/v) with respect to u

The Attempt at a Solution

Using the chain rule

f_u = (1/(1 + (u/v)²)) * 1/v = 1/(v + u²/v)

The solutions manual says v/(u² + v²)

What is my mistake?

Physics news on Phys.org

May 17, 2008

hotcommodity

Multiply the top and bottom of your answer by "v" and see what you get

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

View full post »