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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
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Solution:

268

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[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]

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