d/(d{x)}(({z})(sin({y}{z})-{x}-2{y}-3{z}))

解答

\frac{d}{d x} ((z) (sin (y z) - x - 2 y - 3 z))

- z

求解步骤

\frac{d}{d x} ((z) (sin (y z) - x - 2 y - 3 z))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= z \frac{d}{d x} (sin (y z) - x - 2 y - 3 z)

使用微分加减法定则:

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

= z (\frac{d}{d x} (sin (y z)) - \frac{d}{d x} (x) - \frac{d}{d x} (2 y) - \frac{d}{d x} (3 z))

\frac{d}{d x} (sin (y z)) = 0

\frac{d}{d x} (x) = 1

\frac{d}{d x} (2 y) = 0

\frac{d}{d x} (3 z) = 0

= z (0 - 1 - 0 - 0)

化简

= - z

e x p an d t^{2} e^{t} u (t - 1)

e x p an d lo g_{10} (7) (a^{2} b^{3} c)

e x p an d \frac{x ^{3}}{x ^{10}}

e x p an d cos (θ) (tan (θ) + cot (θ) = csc (θ))

e x p an d F (0, - \frac{1}{2})