derivative of x/(csch(x))

解答

\frac{d}{d x} (\frac{x}{csch ( x )})

sinh (x) + x cosh (x)

求解步骤

\frac{d}{d x} (\frac{x}{csch ( x )})

化简

\frac{x}{csch ( x )} : x sinh (x)

= \frac{d}{d x} (x sinh (x))

使用微分乘法定则:

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

f = x, g = sinh (x)

= \frac{d x}{d x} sinh (x) + \frac{d}{d x} (sinh (x)) x

\frac{d x}{d x} = 1

\frac{d}{d x} (sinh (x)) = cosh (x)

= 1 \cdot sinh (x) + cosh (x) x

化简

= sinh (x) + x cosh (x)

\int 30 x \cdot (x + 1)^{4} d x

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

\int \frac{x ^{4}}{x ^{4} - 16} d x

y^{^{''}} + 9 y = 2 cos (3 x) + 3 sin (3 x)

t an g e n t f (x) = 4 sin (x), at x = \frac{π}{2}