How is the following notation interpreted? $$\frac{d}{dx} (f^3)(1)$$
Does this evaluate to $3\cdot f(1)^2\cdot f'(1) $, or is it simply the derivative of a constant and equal to 0?
2026-05-14 08:42:26.1778748146
How is the notation $\frac{d}{dx} (f^3)(1)$ interpreted?
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I'd say it probably means the derivative of the function $f$ (whatever that function happens to be) cubed evaluated at $1$. And I'd also suggest that it would probably be better to denote $f$ as $f(x)$:
$$ \frac{d}{dx}(f^3)(1) = 3\cdot [f(x)]^2\cdot f'(x)\vert_{x=1}=3\cdot [f(1)]^2\cdot f'(1) $$