Suppose $$ f^{\prime}(5)=3 $$ and $$ g^{\prime}(5)=6 $$ Find $$ h^{\prime}(5) $$ where $$ h(x)=2 f(x)+5 g(x)+5 $$ $$ h^{\prime}(5)=\square $$

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1. The given function is $$ h(x) = 2f(x) + 5g(x) + 5 $$.

2. To find $$ h^{\prime}(x) $$, differentiate each term:
   $$
   h^{\prime}(x) = \frac{d}{dx} \Big[2f(x)\Big] + \frac{d}{dx} \Big[5g(x)\Big] + \frac{d}{dx} \Big[5\Big]
   $$
   
3. Applying the constant multiple rule and the derivative of constant:
   $$
   h^{\prime}(x) = 2f^{\prime}(x) + 5g^{\prime}(x) + 0
   $$
   $$
   h^{\prime}(x) = 2f^{\prime}(x) + 5g^{\prime}(x)
   $$

4. Substitute the given values at $$ x=5 $$:
   $$
   f^{\prime}(5) = 3 \quad \text{and} \quad g^{\prime}(5) = 6
   $$
   $$
   h^{\prime}(5) = 2 \times 3 + 5 \times 6
   $$

5. Calculate the result:
   $$
   h^{\prime}(5) = 6 + 30 = 36
   $$

Thus, $$ h^{\prime}(5)=\boxed{36} $$.
$$ h^{\prime}(5)=36 $$

Suppose \( f^{\prime}(5)=3 \) and \( g^{\prime}(5)=6 \) Find \( h^{\prime}(5) \) where \( h(x)=2 f(x)+5 g(x)+5 \) \( h^{\prime}(5)=\square \)

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