derivative of 4/((x+2^2+16))

解答

\frac{d}{d x} (\frac{4}{( x + 2 ) ^{2} + 16})

- \frac{4 ( 2 x + 4 )}{( x ^{2} + 4 x + 20 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{4}{( x + 2 ) ^{2} + 16})

将常数提出:

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

= 4 \frac{d}{d x} (\frac{1}{( x + 2 ) ^{2} + 16})

使用指数法则:

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

= 4 \frac{d}{d x} (((x + 2)^{2} + 16)^{- 1})

使用连锁律:

- \frac{1}{( ( x + 2 ) ^{2} + 16 ) ^{2}} \frac{d}{d x} ((x + 2)^{2} + 16)

= - \frac{1}{( ( x + 2 ) ^{2} + 16 ) ^{2}} \frac{d}{d x} ((x + 2)^{2} + 16)

\frac{d}{d x} ((x + 2)^{2} + 16) = 2 x + 4

= 4 - \frac{1}{( ( x + 2 ) ^{2} + 16 ) ^{2}} (2 x + 4)

化简

4 - \frac{1}{( ( x + 2 ) ^{2} + 16 ) ^{2}} (2 x + 4) : - \frac{4 ( 2 x + 4 )}{( x ^{2} + 4 x + 20 ) ^{2}}

= - \frac{4 ( 2 x + 4 )}{( x ^{2} + 4 x + 20 ) ^{2}}

\frac{\partial}{\partial x} ((e^{x} - x) cos (y))

\frac{d}{d t} (- 32 t)

\int 25 - x^{2} - 3 d x

x \to 3 + lim (\frac{1}{x + 3})

(x + e^{y}) y^{^{'}} = x e^{- y} - 1