derivative (x^2-9)^2+2

解答

导数

(x^{2} - 9)^{2} + 2

4 x^{3} - 36 x

求解步骤

\frac{d}{d x} ((x^{2} - 9)^{2} + 2)

化简

(x^{2} - 9)^{2} + 2 : x^{4} - 18 x^{2} + 83

= \frac{d}{d x} (x^{4} - 18 x^{2} + 83)

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} (18 x^{2}) + \frac{d}{d x} (83)

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

\frac{d}{d x} (18 x^{2}) = 36 x

\frac{d}{d x} (83) = 0

= 4 x^{3} - 36 x + 0

化简

= 4 x^{3} - 36 x

7 x (x + 3 y) y^{^{'}} = 7 y (x - 3 y)

5 \frac{d r}{d s} = e^{r - 8 s}

\frac{\partial}{\partial x} (4 y^{2} - x^{2})

\int_{- 1}^{5} x^{2} - 4 x - 5 d x

y^{^{'}} + 4 x y^{4} = 0