derivative 4x^{10x^3}

解答

导数

4 x^{10 x^{3}}

40 x^{10 x^{3}} (3 x^{2} ln (x) + x^{2})

求解步骤

\frac{d}{d x} (4 x^{10 x^{3}})

将常数提出:

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

= 4 \frac{d}{d x} (x^{10 x^{3}})

使用指数法则:

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

x^{10 x^{3}} = e^{10 x^{3} l n (x)}

= 4 \frac{d}{d x} (e^{10 x^{3} l n (x)})

使用连锁律:

e^{10 x^{3} l n (x)} \frac{d}{d x} (10 x^{3} ln (x))

= e^{10 x^{3} l n (x)} \frac{d}{d x} (10 x^{3} ln (x))

\frac{d}{d x} (10 x^{3} ln (x)) = 10 (3 x^{2} ln (x) + x^{2})

= 4 e^{10 x^{3} l n (x)} \cdot 10 (3 x^{2} ln (x) + x^{2})

化简

4 e^{10 x^{3} l n (x)} \cdot 10 (3 x^{2} ln (x) + x^{2}) : 40 x^{10 x^{3}} (3 x^{2} ln (x) + x^{2})

= 40 x^{10 x^{3}} (3 x^{2} ln (x) + x^{2})

f (x) = ln (3^{2 - x^{2}})

\int \frac{x + 4}{x + 2} d x

\int (5 x^{3} - 3 x^{2} - 4 x + 50) d x

\int 2 x^{2} - 8 d x

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