f(x) = arctan(x), g(x) = tan(x) とすると、
d/dx arctan(x)
= f'(x)
= 1/g'(f(x)) (∵ g(f(x)) = x のとき、f'(x) = 1/g'(f(x)) )
= 1/( 1 /(cos(f(x)))^2)
= 1/(((cos(f(x)))^2 + (sin(f(x)))^2)/(cos(f(x)))^2)
= 1/( 1 + (sin(f(x))/cos(f(x)))^2)
= 1/( 1 + (tan(f(x)) )^2)
= 1/( 1 + (tan(arctan(x)))^2)
= 1/( 1 + x ^2)
最新の画像［もっと見る］
