derivative of (x^2/(sin(ax)))

解答

\frac{d}{d x} (\frac{x ^{2}}{sin ( a x )})

2 x csc (a x) - a x^{2} cot (a x) csc (a x)

求解步骤

\frac{d}{d x} (\frac{x ^{2}}{sin ( a x )})

化简

\frac{x ^{2}}{sin ( a x )} : x^{2} csc (a x)

= \frac{d}{d x} (x^{2} csc (a x))

使用微分乘法定则:

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

f = x^{2}, g = csc (a x)

= \frac{d}{d x} (x^{2}) csc (a x) + \frac{d}{d x} (csc (a x)) x^{2}

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

\frac{d}{d x} (csc (a x)) = - cot (a x) csc (a x) a

= 2 x csc (a x) + (- cot (a x) csc (a x) a) x^{2}

化简

= 2 x csc (a x) - a x^{2} cot (a x) csc (a x)

d er i v a t i v e \frac{x ^{2}}{( 5 + x ) ^{4}}

x \to - 7 lim (f (x))

\int \frac{28}{4 x + x x} d x

x \to - \frac{1}{2} lim (\frac{6 x - 1}{x})

\int x^{2} 2 x - x^{2} d x