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  • 14-02-2022
  • Mathematics
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  • 14-02-2022

[tex]f'(x) = (7x^{2} - 3x + 2)^{ \frac{7}{2}} (14x - 3)[/tex]

Explanation

Formula :

[tex] \boxed{f(x) = u^{n} \: \rightarrow \: f'(x) = n \times u^{n - 1} \times u'}[/tex]

Step by step :

[tex] \begin{aligned}f(x)&=(7x^{2} - 3x + 2)^{\frac{9}{2}}\\f'(x)&= \frac{9}{2}(7x^{2} - 3x + 2)^{ \frac{9 - 2}{2}} (14x - 3) \\& = \frac{9}{2} (7x^{2} - 3x + 2)^{ \frac{7}{2}} (14x - 3)\end{aligned}[/tex]

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