derivative of 5\sqrt[3]{12x}

解答

\frac{d}{d x} (5 3 12 x)

\frac{5 3 4}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}}}

求解步骤

\frac{d}{d x} (5 3 12 x)

化简

5 3 12 x : 5312 3 x

= \frac{d}{d x} (5312 3 x)

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 5312 \frac{d}{d x} (3 x)

使用根式运算法则:

n a = a^{\frac{1}{n}}

= 5312 \frac{d}{d x} (x^{\frac{1}{3}})

使用幂法则:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 5312 \frac{1}{3} x^{\frac{1}{3} - 1}

化简

5312 \frac{1}{3} x^{\frac{1}{3} - 1} : \frac{5 3 4}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}}}

= \frac{5 3 4}{3 ^{\frac{2}{3}} x ^{\frac{2}{3}}}

\frac{d}{d x} (\frac{2 x ^{3} + 8}{x})

\frac{d}{d x} (8 x cos (x^{2}))

x \to 8 lim ({f (7) g (- 7)})

\int \frac{4 x ^{2} + 8}{2 x ^{2} + 1} d x

\int \frac{1}{x 25 x ^{2} - 4} d x