Let's clarify the problem step by step. ### Given Functions: 1. **Function \( f(u) \)**: - \( f(u) = u^8 \) 2. **Function \( g(x) \)**: - \( g(x) = 3x + 2 \) ### Derivatives: 1. **Derivative of \( f(u) \)**: - \( f'(u) = 8u^7 \) 2. **Derivative of \( g(x) \)**: - \( g'(x) = 3 \) ### Chain Rule: To find the derivative of the composition \( (f \circ g)(x) \), we use the chain rule: \[ (f \circ g)'(x) = f'(g(x)) \cdot g'(x) \] ### Step-by-Step Calculation: 1. **Calculate \( g(x) \)**: - \( g(x) = 3x + 2 \) 2. **Calculate \( f'(g(x)) \)**: - Substitute \( g(x) \) into \( f' \): \[ f'(g(x)) = f'(3x + 2) = 8(3x + 2)^7 \] 3. **Calculate \( g'(x) \)**: - \( g'(x) = 3 \) 4. **Combine using the chain rule**: \[ (f \circ g)'(x) = f'(g(x)) \cdot g'(x) = 8(3x + 2)^7 \cdot 3 = 24(3x + 2)^7 \] ### Assessing Statements: Now, let's evaluate the statements provided in the question: 1. **\( f'(g(x)) \) is incorrect**: **False** (it is correct) 2. **\( f(g(x)) \) is incorrect**: **False** (it is correct, \( f(g(x)) = (3x + 2)^8 \)) 3. **\( g'(x) \) is incorrect**: **False** (it is correct, \( g'(x) = 3 \)) 4. **\( (f \circ g)' \) is incorrect**: **False** (it is correct, \( (f \circ g)'(x) = 24(3x + 2)^7 \)) 5. **\( f'(u) \) is incorrect**: **False** (it is correct, \( f'(u) = 8u^7 \)) ### Summary: All the computations are actually correct. Therefore, none of the statements about the computations being incorrect are true. If you have further questions or need additional clarification, feel free to ask