derivative of (a^2x/((x+b)^2))

解答

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

\frac{a ^{2} ( b - x )}{( x + b ) ^{3}}

求解步骤

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

将常数提出:

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

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

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d x}{d x} = 1

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

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

化简

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

= \frac{a ^{2} ( b - x )}{( x + b ) ^{3}}

\frac{d}{d x} (3 \frac{3 x}{4 π})

x \to - 3 lim (\frac{4 x - 5}{3 x + 9})

x \to 1 lim ([3 x + 1])

\int (1 + 6 x)^{4} (6) d x

\int_{1}^{5} 37 d x