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Chapter 12: Q. 25 (page 964)

Use Theorem 12.32 to find the indicated derivatives in Exercises 21鈥�26. Express your answers as functions of a single variable.

drdtwhenr=x2+y2,x=tandy=t2

Short Answer

Expert verified

The value isdrdt=1+4t32t+t4

Step by step solution

01

Step 1. Given Information:

Given:

r=x2+y2,x=tandy=t2

We have to find the indicated derivatives and express your answers as functions of a single variable.

02

Step 2. Solution:

Usingx=tandy=t2inr=x2+y2wegetr=t2+(t2)2r=t+t4Diff.w.r.t.twegetdrdt=12t+t4路(1+4t3)drdt=1+4t32t+t4

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