derivative of (3x-1^5(1-3x)^4)

解答

\frac{d}{d x} ((3 x - 1)^{5} (1 - 3 x)^{4})

15 (3 x - 1)^{4} (1 - 3 x)^{4} - 12 (1 - 3 x)^{3} (3 x - 1)^{5}

求解步骤

\frac{d}{d x} ((3 x - 1)^{5} (1 - 3 x)^{4})

使用微分乘法定则:

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

f = (3 x - 1)^{5}, g = (1 - 3 x)^{4}

= \frac{d}{d x} ((3 x - 1)^{5}) (1 - 3 x)^{4} + \frac{d}{d x} ((1 - 3 x)^{4}) (3 x - 1)^{5}

\frac{d}{d x} ((3 x - 1)^{5}) = 15 (3 x - 1)^{4}

\frac{d}{d x} ((1 - 3 x)^{4}) = - 12 (1 - 3 x)^{3}

= 15 (3 x - 1)^{4} (1 - 3 x)^{4} + (- 12 (1 - 3 x)^{3}) (3 x - 1)^{5}

化简

= 15 (3 x - 1)^{4} (1 - 3 x)^{4} - 12 (1 - 3 x)^{3} (3 x - 1)^{5}

\int \frac{x ^{2}}{1 - 4 x ^{2}} d x

x \to \infty lim (4 \cdot x)

x \to + 0 + lim (e^{- \frac{2}{x ^{3}}})

d er i v a t i v e f (x) = \frac{x ^{2}}{cos ( x )}

d er i v a t i v e f (x) = tan (5 x)