(\partial)/(\partial t)(6q(r,t)^2+7r^3-8/t-q(r,t)t)

解答

\frac{\partial}{\partial t} (6 q (r, t) (r, t)^{2} + 7 r^{3} - \frac{8}{t} - q (r, t) t)

6 (\frac{\partial}{\partial t} (q (r, t)) (r, t)^{2} + 2 (r, t) (r, 1) q (r, t)) + 0 - (- \frac{8}{t ^{2}}) - (\frac{\partial}{\partial t} (q (r, t)) t + 1 \cdot q (r, t))

求解步骤

\frac{\partial}{\partial t} (6 q (r, t) (r, t)^{2} + 7 r^{3} - \frac{8}{t} - q (r, t) t)

将

r

视为常数

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial t} (6 q (r, t) (r, t)^{2}) + \frac{\partial}{\partial t} (7 r^{3}) - \frac{\partial}{\partial t} (\frac{8}{t}) - \frac{\partial}{\partial t} (q (r, t) t)

\frac{\partial}{\partial t} (6 q (r, t) (r, t)^{2}) = 6 (\frac{\partial}{\partial t} (q (r, t)) (r, t)^{2} + 2 (r, t) (r, 1) q (r, t))

\frac{\partial}{\partial t} (7 r^{3}) = 0

\frac{\partial}{\partial t} (\frac{8}{t}) = - \frac{8}{t ^{2}}

\frac{\partial}{\partial t} (q (r, t) t) = \frac{\partial}{\partial t} (q (r, t)) t + 1 \cdot q (r, t)

= 6 (\frac{\partial}{\partial t} (q (r, t)) (r, t)^{2} + 2 (r, t) (r, 1) q (r, t)) + 0 - (- \frac{8}{t ^{2}}) - (\frac{\partial}{\partial t} (q (r, t)) t + 1 \cdot q (r, t))

n = 0 \sum \infty \frac{2}{n ^{2} + 6 n + 8}

d er i v a t i v e (2 x - 5)^{2}

t a y l or x^{2} cos (x)

d er i v a t i v e sin^{3} (2 x)

\frac{d}{d x} (\frac{2 x ^{2} + 6 x + 8}{x})