(\partial)/(\partial x)(x^5+xy^7+4)

解答

\frac{\partial}{\partial x} (x^{5} + x y^{7} + 4)

5 x^{4} + y^{7}

求解步骤

\frac{\partial}{\partial x} (x^{5} + x y^{7} + 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} (x^{5}) + \frac{\partial}{\partial x} (x y^{7}) + \frac{\partial}{\partial x} (4)

\frac{\partial}{\partial x} (x^{5}) = 5 x^{4}

\frac{\partial}{\partial x} (x y^{7}) = y^{7}

\frac{\partial}{\partial x} (4) = 0

= 5 x^{4} + y^{7} + 0

化简

= 5 x^{4} + y^{7}

\frac{d}{d x} ((ln (x))^{l n (x)})

x \to 7 lim (\frac{x + 4}{x - 7})

d er i v a t i v e f (2) = \frac{x ^{2} - 4}{x - 2}

\frac{d ^{2} x}{d t ^{2}} = - k x

\frac{d}{d x} ((8 x^{2} - 2 x) (5 x + 9))