derivative (3x^2+x)(5x^3+1)

解答

导数

(3 x^{2} + x) (5 x^{3} + 1)

75 x^{4} + 20 x^{3} + 6 x + 1

求解步骤

\frac{d}{d x} ((3 x^{2} + x) (5 x^{3} + 1))

使用微分乘法定则:

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

f = 3 x^{2} + x, g = 5 x^{3} + 1

= \frac{d}{d x} (3 x^{2} + x) (5 x^{3} + 1) + \frac{d}{d x} (5 x^{3} + 1) (3 x^{2} + x)

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

\frac{d}{d x} (5 x^{3} + 1) = 15 x^{2}

= (6 x + 1) (5 x^{3} + 1) + 15 x^{2} (3 x^{2} + x)

化简

(6 x + 1) (5 x^{3} + 1) + 15 x^{2} (3 x^{2} + x) : 75 x^{4} + 20 x^{3} + 6 x + 1

= 75 x^{4} + 20 x^{3} + 6 x + 1

\int \frac{- 1}{e ^{x}} d x

\int x (x^{4} + \frac{1}{4} x) d x

\int y^{3} e^{y^{4}} d y

\frac{d}{d x} (cos ((π x)^{9}))

\frac{\partial}{\partial x} (x^{0.1})