derivative x^2arctan(5x)

解答

导数

x^{2} arctan (5 x)

2 x arctan (5 x) + \frac{5 x ^{2}}{25 x ^{2} + 1}

求解步骤

\frac{d}{d x} (x^{2} arctan (5 x))

使用微分乘法定则:

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

f = x^{2}, g = arctan (5 x)

= \frac{d}{d x} (x^{2}) arctan (5 x) + \frac{d}{d x} (arctan (5 x)) x^{2}

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

\frac{d}{d x} (arctan (5 x)) = \frac{5}{25 x ^{2} + 1}

= 2 x arctan (5 x) + \frac{5}{25 x ^{2} + 1} x^{2}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 x arctan (5 x) + \frac{5 x ^{2}}{25 x ^{2} + 1}

\int e^{\frac{4 x}{9}} (\frac{4}{9}) d x

t an g e n t x^{2} - 4 x

\int sin (\frac{1}{10}) x sin (\frac{1}{20}) x d x

x \to 4 + lim (5 x^{2} + x)

3 x \frac{d y}{d x} = 2 x e^{x} - 3 y + 6 x^{2}