`f(z) = 1/(z^2 + 1)` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 11 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17's profile pic

gsarora17 | (Level 2) Associate Educator

Posted on

f(z)=`1/(z^2+1)`

`f'(z) = -1((z^2+1)^(-1-1))*2z`

`f'(z) = -1(z^2+1)^-2*2z`

`f'(z) = -(2z)/(z^2+1)^2`

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goodthink | Student, Grade 12 | (Level 1) Honors

Posted on

Use a quotient rule:

`f'(z)=((0)(z^(2)+1)-(1)(2z))/((z^(2)+1))^(2) `

This simplifies to:

`f'(z)=(-2z)/(z^(2)+1)^(2) `

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