derivative of (θ(e^θ)(2θ))

解答

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

2 (e^{x} x^{2} + 2 x e^{x})

求解步骤

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

化简

(x) (e^{x}) (2 x) : 2 e^{x} x^{2}

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

将常数提出:

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

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

使用微分乘法定则:

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

f = e^{x}, g = x^{2}

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

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

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

= 2 (e^{x} x^{2} + 2 x e^{x})

f a c t or (a \cdot b) - (c \cdot d)

f a c t or x - b x - y + b y

\int (\frac{d}{d t} (sin (2 t)))^{2} d t

f a c t or \frac{2550}{17000}

f a c t or 27 x^{4} + 40 x^{4} + 3 0^{2}