derivative of cos(arctan(3x))

解答

\frac{d}{d x} (cos (arctan (3 x)))

- \frac{9 x}{( 9 x ^{2} + 1 ) 1 + 9 x ^{2}}

求解步骤

\frac{d}{d x} (cos (arctan (3 x)))

使用连锁律:

- sin (arctan (3 x)) \frac{d}{d x} (arctan (3 x))

= - sin (arctan (3 x)) \frac{d}{d x} (arctan (3 x))

\frac{d}{d x} (arctan (3 x)) = \frac{3}{9 x ^{2} + 1}

= - sin (arctan (3 x)) \frac{3}{9 x ^{2} + 1}

化简

- sin (arctan (3 x)) \frac{3}{9 x ^{2} + 1} : - \frac{9 x}{( 9 x ^{2} + 1 ) 1 + 9 x ^{2}}

= - \frac{9 x}{( 9 x ^{2} + 1 ) 1 + 9 x ^{2}}

\int_{0}^{\frac{1}{10}} x ln (10 x) d x

x \to 0 lim (2)

t an g e n t f (x) = 3 tan (x), at x = \frac{π}{3}

\int_{- \infty}^{0} x d x

\frac{1}{2} \cdot \frac{d y}{d x} = \frac{2 x}{3 y}