Question

反函数导数 已知f(x)的反函数是g(x),当f(x)=x^5+3x^3+x,求g′(5) 写下完整的步骤和推理.

Answer 1

f(x) = x^5+3x^3+x → df(x)/dx = 5x^4+9x^2+1

dg(x)/dx = 1 / [ df(x)/dx ] = 1 / (5x^4+9x^2+1)

由 f(x)=5 得 x=1 ,所以

g′(5) = [ 1 / (5*x^4+9*x^2+1) ] ┃x=1

= 1/15