derivative of |x|^{|cos(x|})

解答

\frac{d}{d x} (∣ x ∣^{∣ c o s (x) ∣})

∣ x ∣^{∣ c o s (x) ∣} (- \frac{cos ( x ) sin ( x ) ln ∣ x ∣}{∣ cos ( x ) ∣} + \frac{∣ cos ( x ) ∣}{x})

求解步骤

\frac{d}{d x} (∣ x ∣^{∣ c o s (x) ∣})

使用指数法则:

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

∣ x ∣^{∣ c o s (x) ∣} = e^{∣ c o s (x) ∣ l n ∣ x ∣}

= \frac{d}{d x} (e^{∣ c o s (x) ∣ l n ∣ x ∣})

使用连锁律:

e^{∣ c o s (x) ∣ l n ∣ x ∣} \frac{d}{d x} (∣ cos (x) ∣ ln ∣ x ∣)

= e^{∣ c o s (x) ∣ l n ∣ x ∣} \frac{d}{d x} (∣ cos (x) ∣ ln ∣ x ∣)

\frac{d}{d x} (∣ cos (x) ∣ ln ∣ x ∣) = - \frac{cos ( x ) sin ( x ) ln ∣ x ∣}{∣ cos ( x ) ∣} + \frac{∣ cos ( x ) ∣}{x}

= e^{∣ c o s (x) ∣ l n ∣ x ∣} (- \frac{cos ( x ) sin ( x ) ln ∣ x ∣}{∣ cos ( x ) ∣} + \frac{∣ cos ( x ) ∣}{x})

e^{∣ c o s (x) ∣ l n ∣ x ∣} = ∣ x ∣^{∣ c o s (x) ∣}

= ∣ x ∣^{∣ c o s (x) ∣} (- \frac{cos ( x ) sin ( x ) ln ∣ x ∣}{∣ cos ( x ) ∣} + \frac{∣ cos ( x ) ∣}{x})

\frac{\partial}{\partial x} (0.5 ln (x) + 0.5 ln (y))

\int e^{8 t} d t

\frac{\partial}{\partial y} ((x + y) e^{x + 2 y})

l a pl a ce t r an s f or m t^{2} - 2 t

d er i v a t i v e - \frac{7}{4 x}