derivative of 1/((1+x^2sqrt(1+x^2)))

解答

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

- \frac{3 x}{( 1 + x ^{2} ) ^{\frac{5}{2}}}

求解步骤

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

使用指数法则:

\frac{1}{a} = a^{- 1}

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

使用连锁律:

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

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

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

= - \frac{1}{( ( 1 + x ^{2} ) 1 + x ^{2} ) ^{2}} \cdot 3 x 1 + x^{2}

化简

- \frac{1}{( ( 1 + x ^{2} ) 1 + x ^{2} ) ^{2}} \cdot 3 x 1 + x^{2} : - \frac{3 x}{( 1 + x ^{2} ) ^{\frac{5}{2}}}

= - \frac{3 x}{( 1 + x ^{2} ) ^{\frac{5}{2}}}

\frac{d}{d x} (sin (x) + \frac{4}{9} cot (x))

x \to 1 lim (F (x))

\int 3 (csc (x))^{2} cot^{3} (x) d x

\int 2 cos (4 x) e^{s i n (4 x)} d x

d er i v a t i v e 2 n d