d/(d{x)}({x}{y}e^{{x}{z}})

解答

\frac{d}{d x} (x y e^{x z})

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

求解步骤

\frac{d}{d x} (x y e^{x z})

将常数提出:

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

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

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{x z}

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

\frac{d}{d x} (x) = 1

\frac{d}{d x} (e^{x z}) = e^{x z} z

= y (1 \cdot e^{x z} + e^{x z} z x)

化简

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

\int_{0}^{3} (x) d x

\frac{d}{d x} (5 x + 6 x^{5})

x \to - 8 lim (- 4 x)

d er i v a t i v e e^{- x} x

y^{^{'}} = \frac{( x ^{4} y ^{4} + x ^{4} )}{y ^{3}}