derivative of A(e^{9x}+9e^{9x}x)

解答

\frac{d}{d x} (A (e^{9 x} + 9 e^{9 x} x))

A (81 e^{9 x} x + 18 e^{9 x})

求解步骤

\frac{d}{d x} (A (e^{9 x} + 9 e^{9 x} x))

将常数提出:

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

= A \frac{d}{d x} (e^{9 x} + 9 e^{9 x} x)

使用微分加减法定则:

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

= A (\frac{d}{d x} (e^{9 x}) + \frac{d}{d x} (9 e^{9 x} x))

\frac{d}{d x} (e^{9 x}) = e^{9 x} \cdot 9

\frac{d}{d x} (9 e^{9 x} x) = 9 (9 e^{9 x} x + e^{9 x})

= A (e^{9 x} \cdot 9 + 9 (9 e^{9 x} x + e^{9 x}))

乘开

e^{9 x} \cdot 9 + 9 (9 e^{9 x} x + e^{9 x}) : 81 e^{9 x} x + 18 e^{9 x}

= A (81 e^{9 x} x + 18 e^{9 x})

x \to 2 lim (2 x - 2)

l a pl a ce t r an s f or m t e^{2 t} cos (5 t)

d er i v a t i v e (10 + sec (θ)) sin (θ)

t a y l or \frac{1}{1 - x}, 8

\frac{d}{d x} (x^{2} ln (x^{5}))