Question

d/dx (2x-3)²
differentiate the following function
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Answer 1

Step-by-step explanation:

this question's answer is 4(2x-3)

Answer 2

$\mathrm \red{Given : }$

$\mathrm{f(x) \: = \: {(2x - 3)}^{2} }$

$\mathrm{By \: differentiating : } \\ \\ \mathrm{ \frac{d}{dx}f(x) \: = \: \frac{d}{dx} \bigg( {(2x - 3).(2x - 3)} \bigg) }$

$\mathrm{f'(x) \: = \: \frac{d}{dx} \bigg( {(2x)}^{2} - 2(2x)(3) + {3}^{2} \bigg) }$

$\mathrm{f'(x) \: = \frac{d}{dx} \bigg( \: 4 {x}^{2} - 12x + 9 \bigg)}$

$\mathrm{f'(x) \: = \: \frac{d}{dx} (4 {x}^{2}) \: - \frac{d}{dx}(12x) + \frac{d}{dx}(9) }$

$\mathrm{f'(x) \: = \: 8x - 12 }$

$\boxed{ \boxed{ \mathsf \red{Formulas \: used : }}} \\ \\ \mathsf{ \frac{d}{dx}( {x}^{n}) \: = \: n. {x}^{n - 1} }$

$\mathsf{ \frac{d}{dx} (u + v + z) \: = \: \frac{d}{dx} (u) + \frac{d}{dx} (v) + \frac{d}{dx} (z)}$