(\partial)/(\partial x)(7^{x^2+1})

解

\frac{\partial}{\partial x} (7^{x^{2} + 1})

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

解答ステップ

\frac{\partial}{\partial x} (7^{x^{2} + 1})

指数の規則を適用する:

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

7^{x^{2} + 1} = e^{(x^{2} + 1) l n (7)}

= \frac{\partial}{\partial x} (e^{(x^{2} + 1) l n (7)})

連鎖法則を適用:

e^{(x^{2} + 1) l n (7)} \frac{\partial}{\partial x} ((x^{2} + 1) ln (7))

= e^{(x^{2} + 1) l n (7)} \frac{\partial}{\partial x} ((x^{2} + 1) ln (7))

\frac{\partial}{\partial x} ((x^{2} + 1) ln (7)) = 2 ln (7) x

= e^{(x^{2} + 1) l n (7)} \cdot 2 ln (7) x

e^{(x^{2} + 1) l n (7)} = 7^{x^{2} + 1}

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