(\partial)/(\partial x)(x*e^{x^2-4})

解答

\frac{\partial}{\partial x} (x \cdot e^{x^{2} - 4})

e^{x^{2} - 4} + 2 e^{x^{2} - 4} x^{2}

求解步骤

\frac{\partial}{\partial x} (x e^{x^{2} - 4})

使用微分乘法定则:

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

f = x, g = e^{x^{2} - 4}

= \frac{\partial}{\partial x} (x) e^{x^{2} - 4} + \frac{\partial}{\partial x} (e^{x^{2} - 4}) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (e^{x^{2} - 4}) = e^{x^{2} - 4} \cdot 2 x

= 1 \cdot e^{x^{2} - 4} + e^{x^{2} - 4} \cdot 2 xx

化简

1 \cdot e^{x^{2} - 4} + e^{x^{2} - 4} \cdot 2 xx : e^{x^{2} - 4} + 2 e^{x^{2} - 4} x^{2}

= e^{x^{2} - 4} + 2 e^{x^{2} - 4} x^{2}

\frac{d}{d x} ((ln (6 x))^{2})

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

d er i v a t i v e f (t) = \frac{2 t}{2 + t}

d er i v a t i v e - cos (t)

t an g e n t x^{3} - x