derivative x^8(x-4)^7

解答

导数

x^{8} (x - 4)^{7}

8 x^{7} (x - 4)^{7} + 7 (x - 4)^{6} x^{8}

求解步骤

\frac{d}{d x} (x^{8} (x - 4)^{7})

使用微分乘法定则:

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

f = x^{8}, g = (x - 4)^{7}

= \frac{d}{d x} (x^{8}) (x - 4)^{7} + \frac{d}{d x} ((x - 4)^{7}) x^{8}

\frac{d}{d x} (x^{8}) = 8 x^{7}

\frac{d}{d x} ((x - 4)^{7}) = 7 (x - 4)^{6}

= 8 x^{7} (x - 4)^{7} + 7 (x - 4)^{6} x^{8}

\frac{d}{d x} (cos (2^{3 x^{2} + 5 x - 6}))

y^{^{'}} = y (x y^{6} + 2)

y^{^{'}} = \frac{4 t ^{3} + 1}{2 y - 6}

\frac{\partial}{\partial y} (x^{2} y^{3} - \frac{1}{1 + 9 x ^{2}})

t an g e n t f (x) = \frac{6}{x - 1}, at x = 3