(\partial)/(\partial x)(x^2+y^2+z^2-25)

解答

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2} - 25)

2 x

求解步骤

\frac{\partial}{\partial x} (x^{2} + y^{2} + z^{2} - 25)

将

y, z

视为常数

使用微分加减法定则:

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

= \frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (z^{2}) - \frac{\partial}{\partial x} (25)

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (z^{2}) = 0

\frac{\partial}{\partial x} (25) = 0

= 2 x + 0 + 0 - 0

化简

= 2 x

y^{^{'}} + 2 y = 2 x + e^{4 x}

\int 2 x cos (9 x) d x

t an g e n t f (x) = \frac{3}{x - 2}, at x = 3

\int_{0}^{4} \frac{3 t}{( t - 5 ) ^{2}} d t

d er i v a t i v e f (x) = \frac{x}{x ^{2} + 6}