derivative f(x)=(x^2)/(1+4x)

解答

导数

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

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

求解步骤

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

使用微分除法定则:

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

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

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

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

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

乘开

2 x (1 + 4 x) - 4 x^{2} : 2 x + 4 x^{2}

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

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

l a pl a ce t r an s f or m e^{4 (t - 3)}

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

\int \frac{1}{1 - 5 x} d x

\frac{d r}{d θ} r = (7 + sec (θ)) sin (θ)