derivative of (7^{10x+1})

解答

\frac{d}{d x} ((7)^{10 x + 1})

10 ln (7) \cdot 7^{10 x + 1}

求解步骤

\frac{d}{d x} ((7)^{10 x + 1})

使用指数法则:

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

7^{10 x + 1} = e^{(10 x + 1) l n (7)}

= \frac{d}{d x} (e^{(10 x + 1) l n (7)})

使用连锁律:

e^{(10 x + 1) l n (7)} \frac{d}{d x} ((10 x + 1) ln (7))

= e^{(10 x + 1) l n (7)} \frac{d}{d x} ((10 x + 1) ln (7))

\frac{d}{d x} ((10 x + 1) ln (7)) = 10 ln (7)

= e^{(10 x + 1) l n (7)} \cdot 10 ln (7)

e^{(10 x + 1) l n (7)} = 7^{10 x + 1}

= 10 ln (7) \cdot 7^{10 x + 1}

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