Curves4. Find the derivative y' for each of the followingor functions. You do not need to simplify youranswers. Now you can choose which method youwant to use to find the derivative. Show worka._y=C.b y = (e ² + 4x²¹³) (2 + √x )x -2x)+5x4y=2x² - 4x+17x+4

Given Expression: y=1x3-2ln(x)+5x4 .........(1) y=ex-4x-3(2+x .........(2) y=2x2-4x+17x+4…

Answered: Find the derivative y' for each of the…

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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Question

Curves
4. Find the derivative y' for each of the following
or functions. You do not need to simplify your
answers. Now you can choose which method you
want to use to find the derivative. Show work
a.
_y=
C.
b y = (e ² + 4x²¹³) (2 + √x )
x -
2x)+5x4
y=
2x² - 4x+1
7x+4

Expert Solution

Step 1

Given Expression:

$y = \frac{1}{x^{3}} - 2 \ln (x) + 5 x^{4} . . . . . . . . . (1)$

$y = (e^{x} - 4 x^{- 3}) ((2 + \sqrt{x}) . . . . . . . . . (2)$

$y = \frac{2 x^{2} - 4 x + 1}{7 x + 4} . . . . . . . . . . (3)$

Formulas of derivation:

$\frac{d}{d x} (x^{n}) = n x^{n - 1} \frac{d}{d x} (x y) = y \frac{d x}{d x} + x \frac{d y}{d x} \frac{d}{d x} (\frac{x}{y}) = \frac{y \frac{d x}{d x} + x \frac{d y}{d x}}{y^{2}}$

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Find the derivative y' for each of the following curves or functions. You do not need to simplify your answers. Now you can choose which method you want to use to find the derivative. Show work a. - y = x³ = 2 ln (x) + 5x" by = (e ² + 4x²³²) (2 + √x) C. 2x²2²-4x+1 y= 7x+4