derivative of (3x-1/(sqrt(x^2+2)))

解答

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

\frac{x + 6}{( x ^{2} + 2 ) x ^{2} + 2}

求解步骤

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

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

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

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

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

化简

\frac{3 x ^{2} + 2 - \frac{x}{x ^{2} + 2} ( 3 x - 1 )}{( x ^{2} + 2 ) ^{2}} : \frac{x + 6}{( x ^{2} + 2 ) x ^{2} + 2}

= \frac{x + 6}{( x ^{2} + 2 ) x ^{2} + 2}

\frac{d}{d x} (sin (8 cos (x)))

\int \frac{tan ^{3} ( θ )}{cos ^{4} ( θ )} d θ

x y^{^{''}} + y^{^{'}} = 0

\frac{d}{d x} (π^{x})

\frac{\partial}{\partial x} (\frac{sin ( x )}{x})