高数求导求cos[f(x^2)]的二阶导

求cos[f(x^2)]的二阶导
2025年03月22日 20:51
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网友(1):

y=cosf(x²)
y'=-sinf(x²) *f'(x²)*2x=-2xf'(x²)sinf(x²)
y"=-2[f'(x²)sinf(x²)+2x²f"(x²)sinf(x²)+xf'(x²)cosf(x²)*f'(x²)*2x]
=-2[f'(x²)sinf(x²)+2x²f"(x²)sinf(x²)+2x²f'²(x²)cosf(x²)]