derivative of e^x(2x+3^3)

解答

\frac{d}{d x} (e^{x} (2 x + 3)^{3})

e^{x} (2 x + 3)^{3} + 6 (2 x + 3)^{2} e^{x}

求解步骤

\frac{d}{d x} (e^{x} (2 x + 3)^{3})

使用微分乘法定则:

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

f = e^{x}, g = (2 x + 3)^{3}

= \frac{d}{d x} (e^{x}) (2 x + 3)^{3} + \frac{d}{d x} ((2 x + 3)^{3}) e^{x}

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

\frac{d}{d x} ((2 x + 3)^{3}) = 6 (2 x + 3)^{2}

= e^{x} (2 x + 3)^{3} + 6 (2 x + 3)^{2} e^{x}

\frac{d ^{2}}{d x ^{2}} (e^{\frac{3}{x}})

\int \frac{9 x}{x ^{2} + 1} d x

t an g e n t f (x) = 6 x, at x = 1

(16 y^{2} - x y) d x + x^{2} d y = 0

\frac{d}{d x} (9 x - \frac{3}{x})