Let `G(u)=2-u^(3)+u^(5)/5`. Find `G^(')(-2)`.

Answer

To find \( G'(-2) \) for the function \( G(u) = 2 - u^3 + \frac{u^5}{5} \), we will first need to differentiate \( G(u) \) with respect to \( u \).

### Step 1: Differentiate \( G(u) \)

The function \( G(u) \) is given as:
\[ G(u) = 2 - u^3 + \frac{u^5}{5} \]

To find \( G'(u) \), we will differentiate each term:

1. The derivative of the constant \( 2 \) is \( 0 \).
2. The derivative of \( -u^3 \) is \( -3u^2 \).
3. The derivative of \( \frac{u^5}{5} \) is \( \frac{5u^4}{5} = u^4 \).

Putting these together, we have:
\[ G'(u) = 0 - 3u^2 + u^4 = u^4 - 3u^2 \]

### Step 2: Evaluate \( G'(-2) \)

Now we need to evaluate \( G'(-2) \):
\[ G'(-2) = (-2)^4 - 3(-2)^2 \]

Calculating each term:
1. \( (-2)^4 = 16 \)
2. \( (-2)^2 = 4 \), thus \( 3(-2)^2 = 3 \times 4 = 12 \)

Now substituting these values back into the equation:
\[ G'(-2) = 16 - 12 = 4 \]

### Final Answer
Thus, the value of \( G'(-2) \) is:
\[ \boxed{4} \]