consider the function $f(x) = (3 - 2x)^4$.

step 1 of 3: find $f(x)$.

Question

consider the function $f(x) = (3 - 2x)^4$.

step 1 of 3: find $f(x)$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Chain Rule Differentiation", "Power Rule Differentiation" ], "new_concepts": [], "current_concepts": [ "Chain Rule Differentiation", "Power Rule Differentiation" ] } ## Identify the function and differentiation rules $$ f(x) = (3 - 2x)^4 $$ ## Apply the chain rule and power rule $$ \begin{aligned} f'(x) &= 4(3 - 2x)^3 \cdot \frac{d}{dx}(3 - 2x) \ f'(x) &= 4(3 - 2x)^3 \cdot (-2) \end{aligned} $$ ## Simplify the expression $$ f'(x) = -8(3 - 2x)^3 $$ Consider the function $f(x) = (3 - 2x)^4$. Step 1 of 3: Find $f'(x)$. $f'(x) =$ $-8(3 - 2x)^3$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Chain Rule Differentiation" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the function and differentiation rules

Apply the chain rule and power rule

Simplify the expression

Answer: