derivative of sqrt(xsin(x))

解答

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

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

求解步骤

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

使用连锁律:

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

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

\frac{d}{d x} (x sin (x)) = sin (x) + x cos (x)

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

化简

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

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

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

\frac{d}{d x} ((5 x^{2} - 8 x) e^{x})

x^{^{''}} - 0 x^{^{'}} + x = 0

\int 6 d x

\frac{\partial}{\partial y} (\frac{- y}{x ^{2} + y ^{2}})