consider the function (f(x) = (8 - 7x)^6).

step 2 of 3: find (f(1)).

answer 2 points

(f(1) = )

Question

consider the function (f(x) = (8 - 7x)^6).

step 2 of 3: find (f(1)).

answer 2 points

(f(1) = )

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" ], "new_concepts": [], "current_concepts": [ "Chain Rule Differentiation", "Power Rule Differentiation" ] } ## Differentiate the function using the chain rule $$ \begin{aligned} f(x) &= (8 - 7x)^6 \ f'(x) &= 6(8 - 7x)^5 \cdot \frac{d}{dx}(8 - 7x) \ f'(x) &= 6(8 - 7x)^5 \cdot (-7) \ f'(x) &= -42(8 - 7x)^5 \end{aligned} $$ ## Evaluate the derivative at x = 1 $$ \begin{aligned} f'(1) &= -42(8 - 7(1))^5 \ f'(1) &= -42(1)^5 \ f'(1) &= -42 \end{aligned} $$ Consider the function $f(x) = (8 - 7x)^6$. Find $f'(1)$. $f'(1) =$ -42 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Calculus", "Chain Rule Differentiation" ] }

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Question

Explanation:

Differentiate the function using the chain rule

Evaluate the derivative at x = 1

Answer: