Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

Find the derivative of 9x³ + 4x² + x + 3 at x = 3.

Sagot :

Answer:

268

Step-by-step explanation:

Derivative Rule

  • dy/dx (xⁿ) = nxⁿ⁻¹

On deriving,

  • dy/dx = 9x³ + 4x² + x + 3
  • dy/dx = 27x² + 8x + 1

Substitute x = 3

  • dy/dx = 27(3)² + 8(3) + 1
  • dy/dx = 243 + 24  + 1
  • dy/dx = 268
fieryanswererft

Solution:

268

=============================

[tex]\sf \bold{ \rightarrow } \ y = 9x^3 + 4x^2 + x + 3[/tex]

[tex]\sf \bold{ \rightarrow } \ \dfrac{dy}{dx} = \dfrac{d}{dx} ( \ 9x^3 + 4x^2 + x + 3 \ )[/tex]

[tex]| | \ \mathrm{ If \ y = x^n , \ then \ \frac{dy}{dx} = nx^{n-1}} \ | |[/tex]

[tex]\sf derivative \ of \ constant \ is \ always \ 0 \ || \ \sf\dfrac{d}{dx}\left(a\right)=0 \ ||[/tex]

solving step wise

[tex]\sf \bold{ \rightarrow } \ \dfrac{d}{dx} ( 9x^3) + \dfrac{d}{dx}(4x^2) + \dfrac{d}{dx}(x )+ \dfrac{d}{dx}(3 )[/tex]

[tex]\sf \bold{ \rightarrow } \ \sf ( 3(9x^{3-1}) +2(4x^{2-1}) + (1)(x^{1-1} )+ 0[/tex]

[tex]\sf \rightarrow 27x^2+8x+1+0[/tex]

[tex]\sf \rightarrow 27x^2+8x+1[/tex]

when x = 3

[tex]\sf \hookrightarrow 27(3)^2+8(3)+1[/tex]

[tex]\sf \hookrightarrow 243+24+1[/tex]

[tex]\sf \hookrightarrow 268[/tex]

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.