Sec 6.3 Natural Exp Function:
(1 point)
suppose that . Find

Ask by West Huang. in the United States

Jan 19,2025

Question

Sec 6.3 Natural Exp Function: (1 point) suppose that $$ f(x)=12 e^{x}-e x^{e} $$. Find $$ f^{\prime}(3) $$ $$ f^{\prime}(3)=\square $$

UpStudy AI · Accepted Answer

To find $$ f^{\prime}(3) $$ for the function $$ f(x) = 12 e^{x} - e x^{e} $$, follow these steps:

1. **Differentiate $$ f(x) $$:**
   $$
   f'(x) = \frac{d}{dx} \left( 12 e^x \right) - \frac{d}{dx} \left( e x^e \right)
   $$
   $$
   f'(x) = 12 e^x - e \cdot e x^{e-1} = 12 e^x - e^{2} x^{e-1}
   $$

2. **Evaluate at $$ x = 3 $$:**
   $$
   f'(3) = 12 e^{3} - e^{2} \cdot 3^{e-1}
   $$

So, the final answer is:

$$
f^{\prime}(3) = 12 e^{3} - e^{2} \cdot 3^{e-1}
$$
$$ f^{\prime}(3) = 12 e^{3} - e^{2} \cdot 3^{e-1} $$

Sec 6.3 Natural Exp Function:
(1 point)
suppose that . Find

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Sec 6.3 Natural Exp Function: (1 point) suppose that . Find