(\partial)/(\partial x)(A(e^{2x}+2e^{2x}x))

解答

\frac{\partial}{\partial x} (A (e^{2 x} + 2 e^{2 x} x))

A (4 e^{2 x} x + 4 e^{2 x})

求解步骤

\frac{\partial}{\partial x} (A (e^{2 x} + 2 e^{2 x} x))

将常数提出:

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

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

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= A (e^{2 x} \cdot 2 + 2 (2 e^{2 x} x + e^{2 x}))

乘开

e^{2 x} \cdot 2 + 2 (2 e^{2 x} x + e^{2 x}) : 4 e^{2 x} x + 4 e^{2 x}

= A (4 e^{2 x} x + 4 e^{2 x})

t an g e n t (x^{2} + y^{2})^{3} = 8 x^{2} y^{2}, (1, 1)

\frac{\partial}{\partial x} (x^{2} + y^{2} - z^{2})

\int_{- 2}^{- 1} \frac{4}{x ^{2}} d x

s l o p e (13) (1 - 10)

d er i v a t i v e 3 e^{x}