1. $$ [-11 $$ Points $$ ] $$ DETAILS MY NOTES Differentiate the function. $$ g(x)=7 x+8 $$ $$ g^{\prime}(x)=\square $$

Question

UpStudy AI · Accepted Answer

1. We start with the function:
   $$
   g(x) = 7x + 8
   $$

2. To differentiate $$ g(x) $$, we use the linearity of differentiation. The derivative of a sum is the sum of the derivatives.

3. The derivative of $$ 7x $$ with respect to $$ x $$ is $$ 7 $$ because:
   $$
   \frac{d}{dx}(7x) = 7
   $$

4. The derivative of the constant $$ 8 $$ is $$ 0 $$ because:
   $$
   \frac{d}{dx}(8) = 0
   $$

5. Therefore, the derivative of $$ g(x) $$ is:
   $$
   g'(x) = 7 + 0 = 7
   $$

Thus, the final answer is:
$$
g'(x) = 7
$$
$$ g'(x) = 7 $$

1. \( [-11 \) Points \( ] \) DETAILS MY NOTES Differentiate the function. \[ g(x)=7 x+8 \] \( g^{\prime}(x)=\square \)