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

解答

\frac{d}{d x} (A (4 e^{2 x} x + 4 e^{2 x}))

A (8 e^{2 x} x + 12 e^{2 x})

求解步骤

\frac{d}{d x} (A (4 e^{2 x} x + 4 e^{2 x}))

将常数提出:

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

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

使用微分加减法定则:

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

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

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

\frac{d}{d x} (4 e^{2 x}) = 8 e^{2 x}

= A (4 (2 e^{2 x} x + e^{2 x}) + 8 e^{2 x})

乘开

4 (2 e^{2 x} x + e^{2 x}) + 8 e^{2 x} : 8 e^{2 x} x + 12 e^{2 x}

= A (8 e^{2 x} x + 12 e^{2 x})

\frac{d}{d x} ((x^{5} + 2 x) (x^{3} + x^{2} + x + 7))

\int \frac{1}{( x + 3 ) ^{2}} d x

a re a y = 9 x^{2} ln (x), y = 36 ln (x)

l a pl a ce t r an s f or m cos^{2} (t)

x \to - 1 lim (x^{3} + x^{2} - 6 x + 9)