derivative (a+2x)^{7x}

解答

导数

(a + 2 x)^{7 x}

7 (ln (a + 2 x) + \frac{2 x}{a + 2 x}) (a + 2 x)^{7 x}

求解步骤

\frac{d}{d x} ((a + 2 x)^{7 x})

使用指数法则:

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

(a + 2 x)^{7 x} = e^{7 x l n (a + 2 x)}

= \frac{d}{d x} (e^{7 x l n (a + 2 x)})

使用连锁律:

e^{7 x l n (a + 2 x)} \frac{d}{d x} (7 x ln (a + 2 x))

= e^{7 x l n (a + 2 x)} \frac{d}{d x} (7 x ln (a + 2 x))

\frac{d}{d x} (7 x ln (a + 2 x)) = 7 (ln (a + 2 x) + \frac{2 x}{a + 2 x})

= e^{7 x l n (a + 2 x)} \cdot 7 (ln (a + 2 x) + \frac{2 x}{a + 2 x})

e^{7 x l n (a + 2 x)} = (a + 2 x)^{7 x}

= 7 (ln (a + 2 x) + \frac{2 x}{a + 2 x}) (a + 2 x)^{7 x}

d er i v a t i v e \frac{1 - t ^{4}}{4}

d er i v a t i v e \frac{1}{2 ^{x}}

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

d er i v a t i v e x^{\frac{1}{2}} lo g_{10} (x)

d er i v a t i v e \frac{8 x ^{2}}{3}