Differentiate .
Answer and explanation
Correct answer: C.
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.
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- Step 1: Apply the chain rule for the natural logarithm: , with .
- Step 2: Find the derivative of the inner function :
- Step 3: Multiply to obtain the final derivative :
Answer
.
Why not the others: The derivatives frac{1}{3x^2 + 1}, frac{6}{3x^2 + 1}, and frac{3x}{3x^2 + 1} omit or incompletely apply the inner derivative chain rule factor .
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