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

解答

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

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

求解步骤

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

将

t

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用指数法则:

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

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

使用连锁律:

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

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

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

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

化简

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

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

\int x^{3} e^{a x^{4}} d x

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

x \to 4 - lim (\frac{1}{x ^{2} - 16})

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

t an g e n t y = ln (x^{2} - 4 x + 1), (4, 0)