derivative of x^2sqrt(2x+3)

解答

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

\frac{5 x ^{2} + 6 x}{2 x + 3}

求解步骤

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

使用微分乘法定则:

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

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

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

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

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

= 2 x 2 x + 3 + \frac{1}{2 x + 3} x^{2}

化简

2 x 2 x + 3 + \frac{1}{2 x + 3} x^{2} : \frac{5 x ^{2} + 6 x}{2 x + 3}

= \frac{5 x ^{2} + 6 x}{2 x + 3}

a re a x^{2} + 4, - x^{2} - 1, [- 2, 3]

\frac{d}{d x} (arcsec (x^{10}))

\frac{d}{d x} ((cos (π x - 16))^{4})

\int \frac{1}{- x ^{2} - 6 x} d x

a re a x = - y, x = 2 y + 3, y = - 2, y = 1