derivative of (x-x^3^x)

解答

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

(ln (x - x^{3}) + \frac{1 - 3 x ^{2}}{1 - x ^{2}}) (x - x^{3})^{x}

求解步骤

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

使用指数法则:

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

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

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

使用连锁律:

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

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

\frac{d}{d x} (x ln (x - x^{3})) = ln (x - x^{3}) + \frac{1 - 3 x ^{2}}{1 - x ^{2}}

= e^{x l n (x - x^{3})} (ln (x - x^{3}) + \frac{1 - 3 x ^{2}}{1 - x ^{2}})

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

= (ln (x - x^{3}) + \frac{1 - 3 x ^{2}}{1 - x ^{2}}) (x - x^{3})^{x}

x \to - \infty lim (- e^{- x})

\int 12 sin^{2} (t) cos (t) d t

\int (12 x + 5)^{2} d x

n = 1 \sum \infty n 6

t an g e n t sin (9 x) + cos (2 x)