derivative f(x)=x(5x^5-1)

解答

导数

f (x) = x (5 x^{5} - 1)

30 x^{5} - 1

求解步骤

\frac{d}{d x} (x (5 x^{5} - 1))

使用微分乘法定则:

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

f = x, g = 5 x^{5} - 1

= \frac{d x}{d x} (5 x^{5} - 1) + \frac{d}{d x} (5 x^{5} - 1) x

\frac{d x}{d x} = 1

\frac{d}{d x} (5 x^{5} - 1) = 25 x^{4}

= 1 \cdot (5 x^{5} - 1) + 25 x^{4} x

化简

1 \cdot (5 x^{5} - 1) + 25 x^{4} x : 30 x^{5} - 1

= 30 x^{5} - 1

d er i v a t i v e 3 t^{2} + 5 t^{3}

\int x sin (9 x^{2}) d x

\frac{d}{d x} (\frac{x ^{6}}{6} + \frac{1}{16 x ^{4}})

x \to 0 lim (\frac{sin ( 5 x )}{sin ( 9 x )})

\int x (3 x^{2} - 5) d x