Find the derivative of the composite exponential function g(x) = e^(4x^2 - 3).

Answer and explanation

Correct answer: B. 8x * e^(4x^2 - 3)

  1. Step 1: Apply the chain rule for exponential functions: d/dx [e^u] = e^u * (du/dx).
  2. Step 2: Identify the inner exponent: u = 4x^2 - 3.
  3. Step 3: Differentiate the exponent: du/dx = 8x.
  4. Step 4: Multiply terms: g'(x) = 8x * e^(4x^2 - 3).
Answer
8x * e^(4x^2 - 3).
Why not the others: 'e^(4x^2 - 3)' omits the derivative of the inner exponent; '4x e^(4x^2 - 3)' differentiates 4x^2 incorrectly as 4x; '8x^2 e^(4x^2 - 3)' fails to reduce the exponent power during differentiation.

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