derivative of arccot(sqrt(4x))

解答

\frac{d}{d x} (arccot (4 x))

- \frac{1}{x ( 4 x + 1 )}

求解步骤

\frac{d}{d x} (arccot (4 x))

化简

arccot (4 x) : arccot (2 x)

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

使用连锁律:

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

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

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

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

化简

- \frac{1}{( 2 x ) ^{2} + 1} \cdot \frac{1}{x} : - \frac{1}{x ( 4 x + 1 )}

= - \frac{1}{x ( 4 x + 1 )}

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

d er i v a t i v e x^{2} + 2

y^{^{'}} + 3 y = 0, y (0) = 0

\frac{\partial}{\partial x} (e^{(y + 1) x})

d er i v a t i v e f (x) = \frac{x ^{3} + 9 x ^{2} + x - 8}{x}