derivative 7/3 x^3(4x^5-11)^3

解答

导数

\frac{7}{3} x^{3} (4 x^{5} - 11)^{3}

7 x^{2} (4 x^{5} - 11)^{2} (24 x^{5} - 11)

求解步骤

\frac{d}{d x} (\frac{7}{3} x^{3} (4 x^{5} - 11)^{3})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{7}{3} \frac{d}{d x} (x^{3} (4 x^{5} - 11)^{3})

使用微分乘法定则:

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

f = x^{3}, g = (4 x^{5} - 11)^{3}

= \frac{7}{3} (\frac{d}{d x} (x^{3}) (4 x^{5} - 11)^{3} + \frac{d}{d x} ((4 x^{5} - 11)^{3}) x^{3})

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

\frac{d}{d x} ((4 x^{5} - 11)^{3}) = 60 x^{4} (4 x^{5} - 11)^{2}

= \frac{7}{3} (3 x^{2} (4 x^{5} - 11)^{3} + 60 x^{4} (4 x^{5} - 11)^{2} x^{3})

化简

\frac{7}{3} (3 x^{2} (4 x^{5} - 11)^{3} + 60 x^{4} (4 x^{5} - 11)^{2} x^{3}) : 7 x^{2} (4 x^{5} - 11)^{2} (24 x^{5} - 11)

= 7 x^{2} (4 x^{5} - 11)^{2} (24 x^{5} - 11)

d er i v a t i v e - 8 x y

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

s l o p e (- 7, - 4), (- 11, - 2)

y^{^{'}} = \frac{( x ^{2} - y ^{2} )}{x y}, y (2) = 3

t an g e n t f (x) = 7 x - 17, at x = 3