3. f(x) = x^2 + bx, g(x) = e^α x, 求 d/dxf(g(x)) = ? (A) 2α e^2α x + bα e^α x (B) α e^2α x + bα e^α x (C) 2α e^2α x + b e^α x (D) 2α e^2α x + 2bα e^α x

12. 求 \(\int_0^1 t^2 e^{-\alpha t} dt = ?\) (A) \(-e^{-\alpha} \left(\frac{1}{\alpha} + \frac{2}{\alpha^2} + \frac{2}{\alpha^3}\right) + \frac{2}{\alpha^3}\) (B) \(-e^{-\alpha} \left(\frac{1}{\alpha} + \frac{2}{\alpha^2} + \frac{2}{\alpha^3}\right)\) (C) \(e^{-\alpha} \left(\frac{1}{\alpha} + \frac{2}{\alpha^2}\right)\) (D) \(e^{-\alpha} \left(\frac{1}{\alpha} + \frac{1}{\alpha^2} + \frac{1}{\alpha^3}\right)\)

3. \(f(x) = x^2 + bx\), \(g(x) = e^{\alpha x}\), 求 \(\frac{d}{dx}f(g(x)) = ?\)
(A) \(2\alpha e^{2\alpha x} + b\alpha e^{\alpha x}\)
(B) \(\alpha e^{2\alpha x} + b\alpha e^{\alpha x}\)
(C) \(2\alpha e^{2\alpha x} + b e^{\alpha x}\)
(D) \(2\alpha e^{2\alpha x} + 2b\alpha e^{\alpha x}\)

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相關試卷

3. \(f(x) = x^2 + bx\), \(g(x) = e^{\alpha x}\), 求 \(\frac{d}{dx}f(g(x)) = ?\)(A) \(2\alpha e^{2\alpha x} + b\alpha e^{\alpha x}\)(B) \(\alpha e^{2\alpha x} + b\alpha e^{\alpha x}\)(C) \(2\alpha e^{2\alpha x} + b e^{\alpha x}\)(D) \(2\alpha e^{2\alpha x} + 2b\alpha e^{\alpha x}\)

相關試題

相關試卷

3. \(f(x) = x^2 + bx\), \(g(x) = e^{\alpha x}\), 求 \(\frac{d}{dx}f(g(x)) = ?\)
(A) \(2\alpha e^{2\alpha x} + b\alpha e^{\alpha x}\)
(B) \(\alpha e^{2\alpha x} + b\alpha e^{\alpha x}\)
(C) \(2\alpha e^{2\alpha x} + b e^{\alpha x}\)
(D) \(2\alpha e^{2\alpha x} + 2b\alpha e^{\alpha x}\)