derivative of (1-x^2(1+x)^3)

解答

\frac{d}{d x} ((1 - x)^{2} (1 + x)^{3})

- 2 (1 - x) (1 + x)^{3} + 3 (1 + x)^{2} (1 - x)^{2}

求解步骤

\frac{d}{d x} ((1 - x)^{2} (1 + x)^{3})

使用微分乘法定则:

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

f = (1 - x)^{2}, g = (1 + x)^{3}

= \frac{d}{d x} ((1 - x)^{2}) (1 + x)^{3} + \frac{d}{d x} ((1 + x)^{3}) (1 - x)^{2}

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

\frac{d}{d x} ((1 + x)^{3}) = 3 (1 + x)^{2}

= (- 2 (1 - x)) (1 + x)^{3} + 3 (1 + x)^{2} (1 - x)^{2}

化简

= - 2 (1 - x) (1 + x)^{3} + 3 (1 + x)^{2} (1 - x)^{2}

n = 1 \sum \infty \frac{3 n}{- 2 n + 5}

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

d er i v a t i v e 3600 (1 - \frac{t}{60})^{2}

x \to 3 lim (\frac{∣ x + 3 ∣}{x + 3})

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