derivative of (10x+2^x)

解答

\frac{d}{d x} ((10 x + 2)^{x})

(ln (10 x + 2) + \frac{5 x}{5 x + 1}) (10 x + 2)^{x}

求解步骤

\frac{d}{d x} ((10 x + 2)^{x})

使用指数法则:

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

(10 x + 2)^{x} = e^{x l n (10 x + 2)}

= \frac{d}{d x} (e^{x l n (10 x + 2)})

使用连锁律:

e^{x l n (10 x + 2)} \frac{d}{d x} (x ln (10 x + 2))

= e^{x l n (10 x + 2)} \frac{d}{d x} (x ln (10 x + 2))

\frac{d}{d x} (x ln (10 x + 2)) = ln (10 x + 2) + \frac{5 x}{5 x + 1}

= e^{x l n (10 x + 2)} (ln (10 x + 2) + \frac{5 x}{5 x + 1})

e^{x l n (10 x + 2)} = (10 x + 2)^{x}

= (ln (10 x + 2) + \frac{5 x}{5 x + 1}) (10 x + 2)^{x}

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