derivative of x^2(x+3^{10})

解答

\frac{d}{d x} (x^{2} (x + 3)^{10})

2 x (x + 3)^{10} + 10 (x + 3)^{9} x^{2}

求解步骤

\frac{d}{d x} (x^{2} (x + 3)^{10})

使用微分乘法定则:

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

f = x^{2}, g = (x + 3)^{10}

= \frac{d}{d x} (x^{2}) (x + 3)^{10} + \frac{d}{d x} ((x + 3)^{10}) x^{2}

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

\frac{d}{d x} ((x + 3)^{10}) = 10 (x + 3)^{9}

= 2 x (x + 3)^{10} + 10 (x + 3)^{9} x^{2}

a re a y = x^{3} - 2 x^{2} + 2, y = 3 x^{2} + 3 x - 13

\frac{d}{d x} f^{- 1} (x) = 2 x + ln (x + 1)

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

\frac{\partial ^{2}}{\partial x \partial y} (x y^{2} - 6 x^{2} - 3 y^{2})

s l o p e in t erce pt (7.4) (3.8)