derivative of 10^{x^2}

解

\frac{d}{d x} (1 0^{x^{2}})

ln (10) \cdot 5^{x^{2}} \cdot 2^{x^{2} + 1} x

解答ステップ

\frac{d}{d x} (1 0^{x^{2}})

指数の規則を適用する:

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

1 0^{x^{2}} = e^{x^{2} l n (10)}

= \frac{d}{d x} (e^{x^{2} l n (10)})

連鎖法則を適用:

e^{x^{2} l n (10)} \frac{d}{d x} (x^{2} ln (10))

= e^{x^{2} l n (10)} \frac{d}{d x} (x^{2} ln (10))

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

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

簡素化

e^{x^{2} l n (10)} \cdot 2 ln (10) x : ln (10) \cdot 5^{x^{2}} \cdot 2^{x^{2} + 1} x

= ln (10) \cdot 5^{x^{2}} \cdot 2^{x^{2} + 1} x