1. Diketahui f(x) = (3x + 5)2, tentukanlah nilai f'(-2)!
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Diketahui f(x) = (3x + 5)², maka nilai f′(-2) adalah -6
Penjelasan dengan langkah-langkah :
f(x) = (3x + 5)²
f(x) = (3x + 5)(3x + 5)
f(x) = 9x² + 15x + 15x + 25
f(x) = 9x² + 30x + 25
f′(x) = (9)(2)x²⁻¹ + 30x¹⁻¹ + 0
f′(x) = 18x¹ + 30x⁰
f′(x) = 18x + 30(1)
f′(x) = 18x + 30
f′(x) = 18x + 30
f′(-2) = 18(-2) + 30
f′(-2) = -36 + 30
f′(-2) = -6
f(x) = ( 3x + 5 )²
f ( x ) = ( 3x + 5 ) ( 3x + 5 )
f ( x ) = 3x ( 3x + 5 ) + 5 ( 3x + 5 )
f ( x ) = 9x² + 15x + 15x + 25
f ( x ) = 9x² + 30x + 25
f'(x) = ( 2 × 9 )x^(2-1) + ( 1 × 30 )x^(1-1) + ( 25 × 0 )
f'(x) = 18x¹ + 30x⁰ + 0
f'(x) = 18x + 30(1) + 0
f'(x) = 18x + 30
f'(-2) = 18(-2) + 30
f'(-2) = -36 + 30
f'(-2) = -6
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