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Chapter 12: Q. 26 (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.

d胃dtwhen胃=tan鈭�1yx,x=et,andy=e2t

Short Answer

Expert verified

The value isd胃dt=et1+e2t

Step by step solution

01

Step 1. Given Information:

Given:

胃=tan鈭�1yx,x=etandy=e2t

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

02

Step 2. Solution:

Usingx=et,andy=e2tin胃=tan鈭�1yxweget胃=tan鈭�1e2tet胃=tan鈭�1etDiff.w.r.t.twegetd胃dt=11+e2t路etd胃dt=et1+e2t

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