y=f(x^2)/(x^2)求导
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y=f(x^2)/(x^2)求导
![y=f(x^2)/(x^2)求导](/uploads/image/z/15221150-62-0.jpg?t=y%3Df%28x%5E2%29%2F%EF%BC%88x%5E2%EF%BC%89%E6%B1%82%E5%AF%BC)
y=f(x²) /x²
那么
y'= { [f(x²)]' *x² - f(x²) *(x²)'} / x^4
显然
[f(x²)]'=f '(x²) * (x²)'=2x *f '(x²),而(x²)'=2x
于是
y'= { [f(x²)]' *x² - f(x²) *(x²)'} / x^4
= [2x *f '(x²) *x² - 2x *f(x²)] / x^4
=[2x² *f '(x²) - 2f(x²)] / x^3
那么
y'= { [f(x²)]' *x² - f(x²) *(x²)'} / x^4
显然
[f(x²)]'=f '(x²) * (x²)'=2x *f '(x²),而(x²)'=2x
于是
y'= { [f(x²)]' *x² - f(x²) *(x²)'} / x^4
= [2x *f '(x²) *x² - 2x *f(x²)] / x^4
=[2x² *f '(x²) - 2f(x²)] / x^3