d/(d{y)}(({z}(y,x))({x}{y}^5-{x}^2{y}))

解答

\frac{d}{d y} ((z (y, x)) (x y^{5} - x^{2} y))

z (y, x) (5 y^{4} x - x^{2})

求解步骤

\frac{d}{d y} ((z (y, x)) (x y^{5} - x^{2} y))

将常数提出:

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

= z (y, x) \frac{d}{d y} (x y^{5} - x^{2} y)

使用微分加减法定则:

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

= z (y, x) (\frac{d}{d y} (x y^{5}) - \frac{d}{d y} (x^{2} y))

\frac{d}{d y} (x y^{5}) = 5 y^{4} x

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

= z (y, x) (5 y^{4} x - x^{2})

s im pl i f y 3 (3 sin^{2} (x) - 4 cos^{2} (x))

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

\frac{d ^{2}}{d x ^{2}} ((y) (x^{4} + y^{4} - 16))

e x p an d (10 - 6 y) + (x + 3) i

\frac{\partial}{\partial x} ((y) (- 12 x y - 6 y^{5}))