derivative of (6x+5^x)

解答

\frac{d}{d x} ((6 x + 5)^{x})

(ln (6 x + 5) + \frac{6 x}{6 x + 5}) (6 x + 5)^{x}

求解步骤

\frac{d}{d x} ((6 x + 5)^{x})

使用指数法则:

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

(6 x + 5)^{x} = e^{x l n (6 x + 5)}

= \frac{d}{d x} (e^{x l n (6 x + 5)})

使用连锁律:

e^{x l n (6 x + 5)} \frac{d}{d x} (x ln (6 x + 5))

= e^{x l n (6 x + 5)} \frac{d}{d x} (x ln (6 x + 5))

\frac{d}{d x} (x ln (6 x + 5)) = ln (6 x + 5) + \frac{6 x}{6 x + 5}

= e^{x l n (6 x + 5)} (ln (6 x + 5) + \frac{6 x}{6 x + 5})

e^{x l n (6 x + 5)} = (6 x + 5)^{x}

= (ln (6 x + 5) + \frac{6 x}{6 x + 5}) (6 x + 5)^{x}

n = 0 \sum \infty \frac{x ^{n}}{2 n !}

t a y l or e^{(- \frac{x}{2})}, 0

\frac{d}{d x} (e^{x} sin (5 x))

\frac{d}{d x} (100 x^{\frac{3}{4}} y^{\frac{1}{4}})

s l o p e (- 2, 0), (0, - 4)