(\partial)/(\partial x)(42y^8x^5-30y^7x^4)

解答

\frac{\partial}{\partial x} (42 y^{8} x^{5} - 30 y^{7} x^{4})

210 y^{8} x^{4} - 120 y^{7} x^{3}

求解步骤

\frac{\partial}{\partial x} (42 y^{8} x^{5} - 30 y^{7} x^{4})

将

y

视为常数

使用微分加减法定则:

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

= \frac{\partial}{\partial x} (42 y^{8} x^{5}) - \frac{\partial}{\partial x} (30 y^{7} x^{4})

\frac{\partial}{\partial x} (42 y^{8} x^{5}) = 210 y^{8} x^{4}

\frac{\partial}{\partial x} (30 y^{7} x^{4}) = 120 y^{7} x^{3}

= 210 y^{8} x^{4} - 120 y^{7} x^{3}

d er i v a t i v e cos (2 arctan (\frac{x}{2}))

\int \frac{u ^{2}}{u ^{2} - 8 u} d u

\frac{d}{d x} (x^{\frac{1}{3}} (x + 4))

d er i v a t i v e \frac{2}{1 + 3 x + x ^{2}}

(24 + x^{2}) y^{^{'}} - 2 x y = 0