derivative of sqrt(x)*(x^5+x^4+3x+2)

解答

\frac{d}{d x} (x \cdot (x^{5} + x^{4} + 3 x + 2))

\frac{11 x ^{5} + 9 x ^{4} + 9 x + 2}{2 x}

求解步骤

\frac{d}{d x} (x (x^{5} + x^{4} + 3 x + 2))

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{5} + x^{4} + 3 x + 2

= \frac{d}{d x} (x) (x^{5} + x^{4} + 3 x + 2) + \frac{d}{d x} (x^{5} + x^{4} + 3 x + 2) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (x^{5} + x^{4} + 3 x + 2) = 5 x^{4} + 4 x^{3} + 3

= \frac{1}{2 x} (x^{5} + x^{4} + 3 x + 2) + (5 x^{4} + 4 x^{3} + 3) x

化简

\frac{1}{2 x} (x^{5} + x^{4} + 3 x + 2) + (5 x^{4} + 4 x^{3} + 3) x : \frac{11 x ^{5} + 9 x ^{4} + 9 x + 2}{2 x}

= \frac{11 x ^{5} + 9 x ^{4} + 9 x + 2}{2 x}

\frac{\partial ^{2}}{\partial K ( b ) \partial b} (a K (b) (b)^{a} L^{b})

\frac{d y}{d x} - 6 x y = sin (x^{2})

\frac{d}{d x} (\frac{4 x}{( 3 x ^{2} - 1 ) ^{2}})

\int 4 x - 3 x^{2} d x

l a pl a ce t r an s f or m f (t) = t (sin (9 t) + e^{- 2 t})