derivative of (3x/(x+1))

解答

\frac{d}{d x} (\frac{3 x}{x + 1})

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

求解步骤

\frac{d}{d x} (\frac{3 x}{x + 1})

将常数提出:

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

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

使用微分除法定则:

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

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

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

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

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

化简

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

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

d er i v a t i v e x^{2} e^{- 7 x}

a re a y = 5 x, y = \frac{5}{x}, x = 5

\frac{d}{d x} (cos (tan (6 x)))

x \to \infty lim (csc (\frac{1}{x}) - cot (\frac{1}{x}))

y^{^{''}} - 14 y^{^{'}} + 74 y = 0