derivative f(x)=xsqrt(x^3-6)

解答

导数

f (x) = x x^{3} - 6

\frac{5 x ^{3} - 12}{2 x ^{3} - 6}

求解步骤

\frac{d}{d x} (x x^{3} - 6)

使用微分乘法定则:

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

f = x, g = x^{3} - 6

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

\frac{d x}{d x} = 1

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

= 1 \cdot x^{3} - 6 + \frac{3 x ^{2}}{2 x ^{3} - 6} x

化简

1 \cdot x^{3} - 6 + \frac{3 x ^{2}}{2 x ^{3} - 6} x : \frac{5 x ^{3} - 12}{2 x ^{3} - 6}

= \frac{5 x ^{3} - 12}{2 x ^{3} - 6}

d er i v a t i v e y = 2 x^{2} 2 - x

\frac{\partial}{\partial x} (e^{- 1} cos (π x))

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

l a pl a ce t r an s f or m 10 + t^{2}

\int_{0}^{π} sin^{2} (7 x) d x