derivative f(x)=3sqrt(x^3)

解答

导数

f (x) = 3 x^{3}

\frac{9 x}{2}

求解步骤

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

将常数提出:

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

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

使用根式运算法则:

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

= 3 \frac{d}{d x} (x^{\frac{3}{2}})

使用幂法则:

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

= 3 \cdot \frac{3}{2} x^{\frac{3}{2} - 1}

化简

3 \cdot \frac{3}{2} x^{\frac{3}{2} - 1} : \frac{9 x}{2}

= \frac{9 x}{2}

\int_{0}^{8} - x^{2} + 2 x + 4 d x

t an g e n t f (x) = \frac{4 x}{x + 1}, at x = 3

x \to - 4 lim (\frac{∣ x + 4 ∣}{x + 4})

d er i v a t i v e y = (e^{4 x} - 3)^{8}

\frac{d ^{3}}{d x ^{3}} (2 x^{3} - 4 x^{2} + 2)