d/(d{x)}({x}{y}{z}+5/4 {z}^4+e^{{x}}cos({y}))

解答

\frac{d}{d x} (x y z + \frac{5}{4} z^{4} + e^{x} cos (y))

e^{x} cos (y) + y z

求解步骤

\frac{d}{d x} (x y z + \frac{5}{4} z^{4} + e^{x} cos (y))

化简

x y z + \frac{5}{4} z^{4} + e^{x} cos (y) : x y z + \frac{5 z ^{4}}{4} + e^{x} cos (y)

= \frac{d}{d x} (x y z + \frac{5 z ^{4}}{4} + e^{x} cos (y))

使用微分加减法定则:

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

= \frac{d}{d x} (x y z) + \frac{d}{d x} (\frac{5 z ^{4}}{4}) + \frac{d}{d x} (e^{x} cos (y))

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

\frac{d}{d x} (\frac{5 z ^{4}}{4}) = 0

\frac{d}{d x} (e^{x} cos (y)) = cos (y) e^{x}

= y z + 0 + cos (y) e^{x}

化简

= e^{x} cos (y) + y z

x \to 0 lim (x sin (\frac{3}{x}))

\int 1 x^{2} d x

\int \frac{( x - 1 ) ^{2}}{x} d x

\int_{0}^{1} \frac{89}{x ^{5}} d x

x y^{^{'}} + 2 y = x^{3} - 4