derivative of (e^{(x^2}+4)^2)

解答

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

4 e^{x^{2}} x (e^{x^{2}} + 4)

求解步骤

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

使用连锁律:

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

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

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

= 2 (e^{x^{2}} + 4) \cdot 2 e^{x^{2}} x

化简

= 4 e^{x^{2}} x (e^{x^{2}} + 4)

y^{^{''}} - 8 y^{^{'}} + 18 y = 0, y (0) = 1, y^{^{'}} (0) = - 4

\int (8 x^{2} + 5)^{10} x d x

\int 2 x (x^{2} + 7)^{7} d x

\frac{d y}{d x} = - \frac{1}{3} x^{3}

\frac{d ^{2}}{d x ^{2}} (x + \frac{1}{x})