Question

Determine a derivada da função f(x) ​

Answer 1

Resposta:

Se realmente for f(x)=(x²-3)/2x³

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Regra do quociente

f =v/t

f'=(v'*t -v*t')/t²

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f'(x)=[(2x²-3)' *2x³-(x²-3)*(2x³)']/(2x³)²

f'(x)=[(2x) *2x³-(x²-3)*(6x²)]/(4x⁶)

f'(x)=[4x⁴-(6x⁴-18x²)]/(4x⁶)

f'(x)=[4x⁴-6x⁴+18x²]/(4x⁶)

f'(x)=[-2x⁴+18x²]/(4x⁶)

f'(x)=[-x²+9]/(2x⁴) = -  (x²-9)/ (2x⁴)

Letra B