derivative f(x)= 1/6 x^4-6x^2+1

解答

导数

f (x) = \frac{1}{6} x^{4} - 6 x^{2} + 1

\frac{2 x ^{3}}{3} - 12 x

求解步骤

\frac{d}{d x} (\frac{1}{6} x^{4} - 6 x^{2} + 1)

化简

\frac{1}{6} x^{4} - 6 x^{2} + 1 : \frac{x ^{4}}{6} - 6 x^{2} + 1

= \frac{d}{d x} (\frac{x ^{4}}{6} - 6 x^{2} + 1)

使用微分加减法定则:

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

= \frac{d}{d x} (\frac{x ^{4}}{6}) - \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (1)

\frac{d}{d x} (\frac{x ^{4}}{6}) = \frac{2 x ^{3}}{3}

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (1) = 0

= \frac{2 x ^{3}}{3} - 12 x + 0

化简

= \frac{2 x ^{3}}{3} - 12 x

\frac{d}{d x} (9 x sin (π x))

x \to 1 lim (\frac{x ^{6} - 1}{x - 1})

\int_{0}^{1} \frac{9}{x ^{5}} d x

\int \frac{1}{( x ^{2} - 6 x + 11 ) ^{2}} d x

d er i v a t i v e y = - 8^{5 x^{2} - 4}