Consider the following.1- 2x2y =x4 - 2x2 + 4Let u(x) = 1 - 2x2 and v(x) = x* - 2x2 + 4.Find each indicated derivative.u'(x) =v'(x)Find each indicated product.v(x) · u'(x)u(x) · v'(x)dyFinddx

Given: y=1-2x2x4-2x2+4u(x)=1-2x2v(x)=x4-2x2+4 We have to find…

Answered: Consider the following. 1- 2x y = x4 -…

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...

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Related questions

Question

Consider the following.
1- 2x2
y =
x4 - 2x2 + 4
Let u(x) = 1 - 2x2 and v(x) = x* - 2x2 + 4.
Find each indicated derivative.
u'(x) =
v'(x)
Find each indicated product.
v(x) · u'(x)
u(x) · v'(x)
dy
Find
dx

Expert Solution

Step 1

Given:

$\begin{array}{rcl} y & = & \frac{1 - 2 x^{2}}{x^{4} - 2 x^{2} + 4} \\ u (x) & = & 1 - 2 x^{2} \\ v (x) & = & x^{4} - 2 x^{2} + 4 \end{array}$

We have to find

$1 . u' (x) 2 . v' (x) 3 . v (x) \cdot u' (x) 4 . u (x) v' (x) 5 . \frac{d y}{d x}$

The quotient rule of derivative states that $\frac{d}{d x} (\frac{f (x)}{g (x)}) = \frac{g (x) f' (x) - f (x) g' (x)}{{(g (x))}^{2}}$ where $f (x) and g (x)$ are differentiable function.

The product rule of derivative states that $\frac{d}{d x} (f (x) g (x)) = g (x) f' (x) + f (x) g' (x),$ where $f (x) and g (x)$ are differentiable function.

The sum and difference rule of derivative states that $\frac{d}{d x} (f (x) - g (x)) = f' (x) - g' (x)$ , where $f (x) and g (x)$ are differentiable function.