derivative (5t+e^t)(3-sqrt(t))

解答

导数

(5 t + e^{t}) (3 - t)

\frac{- 15 t - 2 e ^{t} t + 6 e ^{t} t - e ^{t}}{2 t} + 15

求解步骤

\frac{d}{d t} ((5 t + e^{t}) (3 - t))

使用微分乘法定则:

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

f = 5 t + e^{t}, g = 3 - t

= \frac{d}{d t} (5 t + e^{t}) (3 - t) + \frac{d}{d t} (3 - t) (5 t + e^{t})

\frac{d}{d t} (5 t + e^{t}) = 5 + e^{t}

\frac{d}{d t} (3 - t) = - \frac{1}{2 t}

= (5 + e^{t}) (3 - t) + (- \frac{1}{2 t}) (5 t + e^{t})

化简

(5 + e^{t}) (3 - t) + (- \frac{1}{2 t}) (5 t + e^{t}) : \frac{- 15 t - 2 e ^{t} t + 6 e ^{t} t - e ^{t}}{2 t} + 15

= \frac{- 15 t - 2 e ^{t} t + 6 e ^{t} t - e ^{t}}{2 t} + 15

(x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}}) (\frac{d x}{d y}) + x^{3} y^{2} = 0

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

\frac{\partial}{\partial x} (x^{2} sin (3 t))

d er i v a t i v e arcsin (e^{2 x})

t^{2} \frac{d y}{d t} + y = 0, y (5) = - 1, t > 0