f(y) = y^(1/n), g(x) = x^m とすると、
d/dx (x^(m/n))
= d/dx ((x^m)^(1/n))
= d/dx f(x^m)
= d/dx f(g(x))
= f'(g(x)) g'(x) (∵ d/dx f(g(x)) = f'(g(x)) g'(x) )
= ((1/n) (g(x))^(1/n - 1)) (m x^(m-1))
= ((1/n) (x^m)^(1/n - 1)) (m x^(m-1))
= ((1/n) x^(m (1/n - 1))) (m x^(m-1))
= (m/n) x^(m (1/n - 1) + (m-1))
= (m/n) x^(m/n - 1)
最新の画像［もっと見る］
