derivative of x^4+12x^2+42

解答

\frac{d}{d x} (x^{4} + 12 x^{2} + 42)

4 x^{3} + 24 x

求解步骤

\frac{d}{d x} (x^{4} + 12 x^{2} + 42)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{4}) + \frac{d}{d x} (12 x^{2}) + \frac{d}{d x} (42)

\frac{d}{d x} (x^{4}) = 4 x^{3}

\frac{d}{d x} (12 x^{2}) = 24 x

\frac{d}{d x} (42) = 0

= 4 x^{3} + 24 x + 0

化简

= 4 x^{3} + 24 x

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

x y^{^{'}} = 2 y + x^{3}

\frac{\partial}{\partial x} (k)

\int \frac{1}{a x ^{2} + b x + c} d x

y^{^{'}} - (\frac{2 x}{1 + x ^{2}}) y = 0, y (0) = 4