derivative of (64x/(x^2+64))

解答

\frac{d}{d x} (\frac{64 x}{x ^{2} + 64})

\frac{64 ( - x ^{2} + 64 )}{( x ^{2} + 64 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{64 x}{x ^{2} + 64})

将常数提出:

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

= 64 \frac{d}{d x} (\frac{x}{x ^{2} + 64})

使用微分除法定则:

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

= 64 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 64 ) - \frac{d}{d x} ( x ^{2} + 64 ) x}{( x ^{2} + 64 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 64) = 2 x

= 64 \cdot \frac{1 \cdot ( x ^{2} + 64 ) - 2 xx}{( x ^{2} + 64 ) ^{2}}

化简

64 \cdot \frac{1 \cdot ( x ^{2} + 64 ) - 2 xx}{( x ^{2} + 64 ) ^{2}} : \frac{64 ( - x ^{2} + 64 )}{( x ^{2} + 64 ) ^{2}}

= \frac{64 ( - x ^{2} + 64 )}{( x ^{2} + 64 ) ^{2}}

\int 4 (1 + tan^{2} (x)) d x

\frac{d y}{d x} = 100 - y

x \to \infty lim ((1 + \frac{1}{2 x + 1})^{x^{2 - 3}})

\int_{0}^{1} (x^{2} - 3 x + 6) d x

x \to 0 lim (+ (x sin (\frac{1}{x})))