(\partial)/(\partial x)(5^{8^{x^2}})

解

\frac{\partial}{\partial x} (5^{8^{x^{2}}})

3 ln (5) ln (2) \cdot 5^{8^{x^{2}}} \cdot 2^{3 x^{2} + 1} x

解答ステップ

\frac{\partial}{\partial x} (5^{8^{x^{2}}})

指数の規則を適用する:

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

5^{8^{x^{2}}} = e^{8^{x^{2}} l n (5)}

= \frac{\partial}{\partial x} (e^{8^{x^{2}} l n (5)})

連鎖法則を適用:

e^{8^{x^{2}} l n (5)} \frac{\partial}{\partial x} (8^{x^{2}} ln (5))

= e^{8^{x^{2}} l n (5)} \frac{\partial}{\partial x} (8^{x^{2}} ln (5))

\frac{\partial}{\partial x} (8^{x^{2}} ln (5)) = 3 ln (5) ln (2) \cdot 2^{3 x^{2} + 1} x

= e^{8^{x^{2}} l n (5)} \cdot 3 ln (5) ln (2) \cdot 2^{3 x^{2} + 1} x

e^{8^{x^{2}} l n (5)} = 5^{8^{x^{2}}}

= 3 ln (5) ln (2) \cdot 5^{8^{x^{2}}} \cdot 2^{3 x^{2} + 1} x