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Taking logarithms turns a variable power into a product: ln y = g·ln f. Differentiating gives y'/y = g'·ln f + g·f'/f, so y' = y(g'·ln f + g·f'/f).
Logarithmic differentiation
y = f^g ⇒ y' = f^g · (g'·ln f + g·f'/f)
y = 64 and y'/y = ln 4 + 3 × 0.5 = 2.8862944, so y' ≈ 184.7228.
The power rule assumes a constant exponent. When the exponent varies, both the base and the exponent contribute.