If f(x) = Ho(2) . ...where g(4) = 0, and g' (4) = 1. then f' (2) =.%3D1+g(x²)%3D%3D%3DO 1/2O 12O-7O-9

The given function is fx=x1+gx2. Obtain the derivative as follows. f'x=ddxx1+gx2=1+gx2 ddxx-x…

Answered: If f(x) = Ho(2) . ... where g(4) = 0,…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Question

If f(x) = Ho(2) . ...
where g(4) = 0, and g' (4) = 1. then f' (2) =.
%3D
1+g(x²)
%3D
%3D
%3D
O 1/2
O 12
O-7
O-9

Expert Solution

Step 1

The given function is $f (x) = \frac{x}{1 + g (x^{2})}$ .

Obtain the derivative as follows.

$\begin{array}{rcl} f' (x) & = & \frac{d}{d x} (\frac{x}{1 + g (x^{2})}) \\ = & \frac{[1 + g (x^{2})] \frac{d}{d x} (x) - x \frac{d}{d x} [1 + g (x^{2})]}{{[1 + g (x^{2})]}^{2}} \\ = & \frac{1 + g (x^{2}) - x g' (x^{2}) (2 x)}{{[1 + g (x^{2})]}^{2}} \\ = & \frac{1 + g (x^{2}) - 2 x^{2} g' (x^{2})}{{[1 + g (x^{2})]}^{2}} \end{array}$