derivative of 6*3^x

解答

\frac{d}{d x} (6 \cdot 3^{x})

2 ln (3) \cdot 3^{1 + x}

求解步骤

\frac{d}{d x} (6 \cdot 3^{x})

化简

6 \cdot 3^{x} : 2 \cdot 3^{1 + x}

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

将常数提出:

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

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

使用指数法则:

a^{b} = e^{b l n (a)}

3^{1 + x} = e^{(1 + x) l n (3)}

= 2 \frac{d}{d x} (e^{(1 + x) l n (3)})

使用连锁律:

e^{(1 + x) l n (3)} \frac{d}{d x} ((1 + x) ln (3))

= e^{(1 + x) l n (3)} \frac{d}{d x} ((1 + x) ln (3))

\frac{d}{d x} ((1 + x) ln (3)) = ln (3)

= 2 e^{(1 + x) l n (3)} ln (3)

e^{(1 + x) l n (3)} = 3^{1 + x}

= 2 ln (3) \cdot 3^{1 + x}

a re a y = 2 - \frac{x}{2}, x = 2 y^{2}

\int (9 x + 2)^{2} d x

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