Please belp me To differentiate or calculate the first differential of f(x)='(x) from firstprinciples means to find the first differential of f(x)=f(x)by using the expressionHenced(f(x))dxf'(x) = -f'(x) = lim8x-0f'(x)= a(f(x))dxSubstitute (x+8x) for x in f(x) = x² to give= lim8x-0f(x+8x)=(x+8x)=x²+2x5x+(8x)²[x²+2x8x+(6x)²-x8x-*}-[f(x+8x)-f(x)\Sx= lim8x-02x8x+(8x)²Sx== lim (2x+8x)5x-0As 8x → 0, [2x + 8x] → 2x, so that the differential of x² is 2x.Hence at x =2, the first differential of the gradient of the curve f'(x) = 4.FindAvalb. f(x) of f(x) = x³+3x²+5x at x=5.5

Answered: Image /qna-images/answer/8138c797-fc9c-4d88-be94-e6ded868eea0.jpg

To differentiate or calculate the first differential of f(x)='(x) from first principles means to find the first differential of f(x)=f(x) by using the expression Hence d(f(x)) dx f'(x) = - f'(x) = Substitute (x+8x) for x in f(x) = x² to give f'(x) = lim 8x-0 d(f(x)) f(x+8x)-f(x)\ dx Sx f(x+8x)=(x+6x)=x²+2x6x+(8x)² = lim 8x->0 x²+2x8x+(6x)²-x² 8x lim 8x-0 2x8x+(8x)'] Sx au ->> As 8x → 0, [2x + 8x] →→ 2x, so that the differential of x² is 2x. Hence at x =2, the first differential of the gradient of the curve f'(x) = 4. Find lim (2x+8x) dx-0 b. f(x) of f(x) = x³+3x²+5x at x=5.5

To differentiate or calculate the first differential of f(x)='(x) from first principles means to find the first differential of f(x)=f(x) by using the expression Hence d(f(x)) dx f'(x) = - f'(x) = Substitute (x+8x) for x in f(x) = x² to give f'(x) = lim 8x-0 d(f(x)) f(x+8x)-f(x)\ dx Sx f(x+8x)=(x+6x)=x²+2x6x+(8x)² = lim 8x->0 x²+2x8x+(6x)²-x² 8x lim 8x-0 2x8x+(8x)'] Sx au ->> As 8x → 0, [2x + 8x] →→ 2x, so that the differential of x² is 2x. Hence at x =2, the first differential of the gradient of the curve f'(x) = 4. Find lim (2x+8x) dx-0 b. f(x) of f(x) = x³+3x²+5x at x=5.5

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

Similar questions

Please state whether this is true or false.
Hi, need help asap! thanks
kindly answer it
Can i get you alls help with the attached?
I just need help with letter d