derivative f(x)=6^{7x^2}

解答

导数

f (x) = 6^{7 x^{2}}

7 ln (6) \cdot 218 7^{x^{2}} \cdot 2^{7 x^{2} + 1} x

求解步骤

\frac{d}{d x} (6^{7 x^{2}})

化简

6^{7 x^{2}} : 27993 6^{x^{2}}

= \frac{d}{d x} (27993 6^{x^{2}})

使用指数法则:

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

27993 6^{x^{2}} = e^{x^{2} l n (279936)}

= \frac{d}{d x} (e^{x^{2} l n (279936)})

使用连锁律:

e^{x^{2} l n (279936)} \frac{d}{d x} (x^{2} ln (279936))

= e^{x^{2} l n (279936)} \frac{d}{d x} (x^{2} ln (279936))

\frac{d}{d x} (x^{2} ln (279936)) = 14 ln (6) x

= e^{x^{2} l n (279936)} \cdot 14 ln (6) x

化简

e^{x^{2} l n (279936)} \cdot 14 ln (6) x : 7 ln (6) \cdot 218 7^{x^{2}} \cdot 2^{7 x^{2} + 1} x

= 7 ln (6) \cdot 218 7^{x^{2}} \cdot 2^{7 x^{2} + 1} x

\int - \frac{1}{x + 1} d x

\frac{\partial}{\partial x} (x^{2} y - 3 y^{4})

\frac{d}{d x} (\frac{1}{5} (x y^{2} + 4 y)^{2})

f (x) = \frac{1}{2 x ^{3}}

\frac{d}{d x} (ln (\frac{x}{x ^{2} + 5}))