derivative of (2-x+3x^2(x^3+5e^x))

解答

\frac{d}{d x} ((2 - x + 3 x^{2}) (x^{3} + 5 e^{x}))

15 x^{4} - 4 x^{3} + 6 x^{2} + 15 e^{x} x^{2} + 25 e^{x} x + 5 e^{x}

求解步骤

\frac{d}{d x} ((2 - x + 3 x^{2}) (x^{3} + 5 e^{x}))

使用微分乘法定则:

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

f = 2 - x + 3 x^{2}, g = x^{3} + 5 e^{x}

= \frac{d}{d x} (2 - x + 3 x^{2}) (x^{3} + 5 e^{x}) + \frac{d}{d x} (x^{3} + 5 e^{x}) (2 - x + 3 x^{2})

\frac{d}{d x} (2 - x + 3 x^{2}) = 6 x - 1

\frac{d}{d x} (x^{3} + 5 e^{x}) = 3 x^{2} + 5 e^{x}

= (6 x - 1) (x^{3} + 5 e^{x}) + (3 x^{2} + 5 e^{x}) (2 - x + 3 x^{2})

化简

(6 x - 1) (x^{3} + 5 e^{x}) + (3 x^{2} + 5 e^{x}) (2 - x + 3 x^{2}) : 15 x^{4} - 4 x^{3} + 6 x^{2} + 15 e^{x} x^{2} + 25 e^{x} x + 5 e^{x}

= 15 x^{4} - 4 x^{3} + 6 x^{2} + 15 e^{x} x^{2} + 25 e^{x} x + 5 e^{x}

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

s l o p e (0) (4.2)

\int \frac{- 5}{( x + 2 ) ^{2}} d x

\int - x^{2} + 2 d x

d er i v a t i v e \frac{10}{x ^{2} + 1}