derivative of (f(x(6x))^2-2)

解答

\frac{d}{d x} ((f (x) (6 x))^{2} - 2)

36 (2 x^{2} f (x) \frac{d}{d x} (f (x)) + 2 x f (x)^{2})

求解步骤

\frac{d}{d x} ((f (x) (6 x))^{2} - 2)

化简

(f (x) (6 x))^{2} - 2 : 36 x^{2} f (x)^{2} - 2

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

使用微分加减法定则:

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

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

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

\frac{d}{d x} (2) = 0

= 36 (2 x f (x)^{2} + 2 f (x) \frac{d}{d x} (f (x)) x^{2}) - 0

化简

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

x \to 0 + lim (2 + ln (x))

d er i v a t i v e sin (x) \cdot tan (x)

a re a f (x) = x^{5} + 4, g (x) = x + 4

t an g e n t f (x) = - \frac{1}{2 1 - x}, at x = - 8

f^{^{'}} (x) = \frac{8 x ^{5} - 6 x ^{9}}{x ^{4}}