derivative of x^2y^4

解答

\frac{d}{d x} (x^{2} y^{4})

2 x y^{4} + 4 y^{3} \frac{d y}{d x} x^{2}

求解步骤

\frac{d}{d x} (x^{2} y^{4})

使用微分乘法定则:

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

f = x^{2}, g = y^{4}

= \frac{d}{d x} (x^{2}) y^{4} + \frac{d}{d x} (y^{4}) x^{2}

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

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

= 2 x y^{4} + 4 y^{3} \frac{d y}{d x} x^{2}

x \to 2 lim (x^{2} - 5)

x \to 0 lim (\frac{1 - e ^{- x}}{x})

\frac{d}{d x} (\frac{x ^{2}}{x ^{3}})

d er i v a t i v e e^{x} (x^{2} + 1) (x + 4)

a re a y = - x, y = - x^{2} + e x