Hello, please explain thoroughly and answer this question, thank you! For the function y = 4x, find5.4d'y4

Given functiony=4x5differentiate with respective xdydx=ddx(4x5)dydx=4ddx(x5)dydx=4*5x5-1…

Answered: d*y For the function y = 4x, find 4

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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Hello, please explain thoroughly and answer this question, thank you!

For the function y = 4x, find
5.
4
d'y
4

Expert Solution

Step 1

$G i v e n f u n c t i o n y = 4 x^{5} d i f f e r e n t i a t e w i t h r e s p e c t i v e x \frac{d y}{d x} = \frac{d}{d x} (4 x^{5}) \frac{d y}{d x} = 4 \frac{d}{d x} (x^{5}) \frac{d y}{d x} = 4 * 5 x^{5 - 1} (\frac{d}{d x} x^{n} = n x^{n - 1}) \frac{d y}{d x} = 4 * 5 x^{4} a g a i n d i f f e r e n t i a t e w i t h r e s p e c t i v e x \frac{d^{2} y}{d x^{2}} = 20 \frac{d}{d x} (x^{4}) \frac{d^{2} y}{d x^{2}} = 20 * 4 x^{4 - 1} \frac{d^{2} y}{d x^{2}} = 80 (x^{3}) a g a i n d i f f e r e n t i a t e w i t h r e s p e c t i v e x \frac{d^{3} y}{d x^{3}} = 80 \frac{d}{d x} (x^{3}) \frac{d^{3} y}{d x^{3}} = 80 * 3 (x^{3 - 1}) \frac{d^{3} y}{d x^{3}} = 240 (x^{2}) a g a i n d i f f e r e n t i a t e w i t h r e s p e c t i v e x \frac{d^{4} y}{d x^{4}} = 240 * \frac{d}{d x} x^{2} \frac{d^{4} y}{d x^{4}} = 240 * 2 x^{2 - 1} \frac{d^{4} y}{d x^{4}} = 480 x$