derivative (1+2x)^x

解答

导数

(1 + 2 x)^{x}

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

求解步骤

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

使用指数法则:

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

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

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

使用连锁律:

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

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

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

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

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

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

d er i v a t i v e (3^{x})^{2}

d er i v a t i v e x tan (3 x^{2} + 4 x + 1)

d er i v a t i v e x^{2} (x + 1)

d er i v a t i v e n + 1

\frac{d}{d s} (2 s)