derivative of (2(x^2(6-x)^3))

解答

\frac{d}{d x} ((2) (x^{2} (6 - x)^{3}))

2 (2 x (6 - x)^{3} - 3 x^{2} (6 - x)^{2})

求解步骤

\frac{d}{d x} ((2) (x^{2} (6 - x)^{3}))

将常数提出:

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

= 2 \frac{d}{d x} (x^{2} (6 - x)^{3})

使用微分乘法定则:

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

f = x^{2}, g = (6 - x)^{3}

= 2 (\frac{d}{d x} (x^{2}) (6 - x)^{3} + \frac{d}{d x} ((6 - x)^{3}) x^{2})

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

\frac{d}{d x} ((6 - x)^{3}) = - 3 (6 - x)^{2}

= 2 (2 x (6 - x)^{3} + (- 3 (6 - x)^{2}) x^{2})

化简

= 2 (2 x (6 - x)^{3} - 3 x^{2} (6 - x)^{2})

e x p an d (8 - 8 x)^{2}

e x p an d \frac{625000 ( 3 + 2 e ^{10} )}{7 e ^{5}}

e x p an d (1 + e^{- x}) e^{x}

s im pl i f y 5 \cdot (x + 7 + 149) (x + 7 - 149)

e x p an d \frac{- x + 1}{( x + 1 ) ^{3}}