derivative of x^2y^5

解答

\frac{d}{d x} (x^{2} y^{5})

2 x y^{5} + 5 y^{4} \frac{d y}{d x} x^{2}

求解步骤

\frac{d}{d x} (x^{2} y^{5})

使用微分乘法定则:

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

f = x^{2}, g = y^{5}

= \frac{d}{d x} (x^{2}) y^{5} + \frac{d}{d x} (y^{5}) x^{2}

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

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

= 2 x y^{5} + 5 y^{4} \frac{d y}{d x} x^{2}

\int_{0}^{\infty} (a + f (x)) d x

d er i v a t i v e ln (64 sin^{2} (x))

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

\int e^{x} cos (a x) d x

x \to + 4 lim (\frac{2}{( x + 4 ) ^{3}})