derivative (x+3)^{3x-2}

解答

导数

(x + 3)^{3 x - 2}

(3 ln (x + 3) + \frac{3 x - 2}{x + 3}) (x + 3)^{3 x - 2}

求解步骤

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

使用指数法则:

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

(x + 3)^{3 x - 2} = e^{(3 x - 2) l n (x + 3)}

= \frac{d}{d x} (e^{(3 x - 2) l n (x + 3)})

使用连锁律:

e^{(3 x - 2) l n (x + 3)} \frac{d}{d x} ((3 x - 2) ln (x + 3))

= e^{(3 x - 2) l n (x + 3)} \frac{d}{d x} ((3 x - 2) ln (x + 3))

\frac{d}{d x} ((3 x - 2) ln (x + 3)) = 3 ln (x + 3) + \frac{3 x - 2}{x + 3}

= e^{(3 x - 2) l n (x + 3)} (3 ln (x + 3) + \frac{3 x - 2}{x + 3})

e^{(3 x - 2) l n (x + 3)} = (x + 3)^{3 x - 2}

= (3 ln (x + 3) + \frac{3 x - 2}{x + 3}) (x + 3)^{3 x - 2}

t an g e n t y = \frac{1}{x - 5}, (4, - 1)

\frac{d}{d y} (\frac{1}{y} e^{x y})

y^{2} = (x y y^{^{'}} + 1) ln (x)

y^{^{'}} = 1 - y

t^{2} y^{^{'}} + 6 t y - y^{3} = 0