Question

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

Answer 1

268

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

Answer 2

268

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`\sf \bold{ \rightarrow } \ y = 9x^3 + 4x^2 + x + 3`

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

`| | \ \mathrm{ If \ y = x^n , \ then \ (dy)/(dx) = nx^(n-1)} \ | |`

`\sf derivative \ of \ constant \ is \ always \ 0 \ || \ \sf(d)/(dx)\left(a\right)=0 \ ||`

solving step wise

`\sf \bold{ \rightarrow } \ (d)/(dx) ( 9x^3) + (d)/(dx)(4x^2) + (d)/(dx)(x )+ (d)/(dx)(3 )`

`\sf \bold{ \rightarrow } \ \sf ( 3(9x^(3-1)) +2(4x^(2-1)) + (1)(x^(1-1) )+ 0`

`\sf \rightarrow 27x^2+8x+1+0`

`\sf \rightarrow 27x^2+8x+1`

when x = 3

`\sf \hookrightarrow 27(3)^2+8(3)+1`

`\sf \hookrightarrow 243+24+1`

`\sf \hookrightarrow 268`