derivative of sqrt(sin(3x))

解答

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

\frac{3 cos ( 3 x )}{2 sin ( 3 x )}

求解步骤

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

使用连锁律:

\frac{1}{2 sin ( 3 x )} \frac{d}{d x} (sin (3 x))

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

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= \frac{1}{2 sin ( 3 x )} cos (3 x) \cdot 3

化简

\frac{1}{2 sin ( 3 x )} cos (3 x) \cdot 3 : \frac{3 cos ( 3 x )}{2 sin ( 3 x )}

= \frac{3 cos ( 3 x )}{2 sin ( 3 x )}

f^{^{'}} (x) = - \frac{4 x}{( 1 + 2 x ^{2} ) ^{2}}

(6 y + 2 x - 7) d x + (4 y + 6 x - 1) d y = 0

\int_{- 1}^{1} 2 - ∣ x ∣ d x

\int \frac{1}{e ^{- t}} d t

\int 4 cos^{3} (6 x) d x