derivative \sqrt[7]{t}+2sqrt(t^7)

解答

导数

7 t + 2 t^{7}

\frac{1 + 49 t ^{\frac{47}{14}}}{7 t ^{\frac{6}{7}}}

求解步骤

\frac{d}{d t} (7 t + 2 t^{7})

使用微分加减法定则:

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

= \frac{d}{d t} (7 t) + \frac{d}{d t} (2 t^{7})

\frac{d}{d t} (7 t) = \frac{1}{7 t ^{\frac{6}{7}}}

\frac{d}{d t} (2 t^{7}) = 7 t^{\frac{5}{2}}

= \frac{1}{7 t ^{\frac{6}{7}}} + 7 t^{\frac{5}{2}}

化简

\frac{1}{7 t ^{\frac{6}{7}}} + 7 t^{\frac{5}{2}} : \frac{1 + 49 t ^{\frac{47}{14}}}{7 t ^{\frac{6}{7}}}

= \frac{1 + 49 t ^{\frac{47}{14}}}{7 t ^{\frac{6}{7}}}

\frac{d}{d x} (x f (x) + f (x) (c x) + c f (x))

\int_{1}^{2} - x + \frac{85}{50} d x

\int tan^{2} (x) \cdot sec^{3} (x) d x

\frac{\partial}{\partial x} (ln (x + 4 y + 9 z))

t an g e n t y = 6 x - x^{2}, (1, 5)