derivative of e^x(2x^4-1)

解答

\frac{d}{d x} (e^{x} (2 x^{4} - 1))

e^{x} (2 x^{4} - 1) + 8 x^{3} e^{x}

求解步骤

\frac{d}{d x} (e^{x} (2 x^{4} - 1))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = 2 x^{4} - 1

= \frac{d}{d x} (e^{x}) (2 x^{4} - 1) + \frac{d}{d x} (2 x^{4} - 1) e^{x}

\frac{d}{d x} (e^{x}) = e^{x}

\frac{d}{d x} (2 x^{4} - 1) = 8 x^{3}

= e^{x} (2 x^{4} - 1) + 8 x^{3} e^{x}

\frac{d ^{2}}{d x ^{2}} (2 x)

\int x \cdot ln (x) d x

\int_{- 4}^{0} (1 + 16 - x^{2}) d x

\int t^{2} 13 t - 1 d t

d er i v a t i v e f (x) = (\frac{4}{x}) + (\frac{1}{5 x ^{3} + 2 x})