derivative (t+e^t)(9-sqrt(t))

解答

导数

(t + e^{t}) (9 - t)

\frac{- 3 t - 2 e ^{t} t + 18 e ^{t} t - e ^{t}}{2 t} + 9

求解步骤

\frac{d}{d t} ((t + e^{t}) (9 - t))

使用微分乘法定则:

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

f = t + e^{t}, g = 9 - t

= \frac{d}{d t} (t + e^{t}) (9 - t) + \frac{d}{d t} (9 - t) (t + e^{t})

\frac{d}{d t} (t + e^{t}) = 1 + e^{t}

\frac{d}{d t} (9 - t) = - \frac{1}{2 t}

= (1 + e^{t}) (9 - t) + (- \frac{1}{2 t}) (t + e^{t})

化简

(1 + e^{t}) (9 - t) + (- \frac{1}{2 t}) (t + e^{t}) : \frac{- 3 t - 2 e ^{t} t + 18 e ^{t} t - e ^{t}}{2 t} + 9

= \frac{- 3 t - 2 e ^{t} t + 18 e ^{t} t - e ^{t}}{2 t} + 9

3 y^{^{'''}} + 12 y^{^{''}} + 12 y^{^{'}} = 0

\int_{0}^{1} (x^{2} + x) e^{x} d x

\int_{0}^{1} e^{- t^{2}} d t

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 0

d er i v a t i v e sec^{2} (2 x + 5) \cdot 2