Find f'(x), if f(x) = (x − 2)2 (2x − 3).

1.	Find f'(x), if f(x) = (x − 2)2 (2x − 3).
Answer» Given, f(x) = (x−2)² (2x−3) = (x²−4x+4)(2x−3) = 2x³ − 8x² + 8x − 3x² + 12x − 12 = 2x³ − 11x² + 20x − 12. f'(x) = \(\frac{d}{dx}\){2x³−11x²+20x−12} \(=2\frac{d}{dx}x^3-11\frac{d}{dx}x^2+20\frac{d}{dx}x-\frac{d}{dx}12\) \(=2.3x^2-11.2x+20.1-0\) \(=6x^2-22x+20\)

Answer»

Given,

f(x) = (x−2)² (2x−3)

= (x²−4x+4)(2x−3)

= 2x³ − 8x² + 8x − 3x² + 12x − 12

= 2x³ − 11x² + 20x − 12.

f'(x) = \(\frac{d}{dx}\){2x³−11x²+20x−12}

\(=2\frac{d}{dx}x^3-11\frac{d}{dx}x^2+20\frac{d}{dx}x-\frac{d}{dx}12\)

\(=2.3x^2-11.2x+20.1-0\)

\(=6x^2-22x+20\)

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