Question

derivada de 16−9 x^ 4/ 3 x^ 2 +4

Answer 1

Primero vamos a desarrollar la expresión:

$f(x)=\dfrac{16-9x^4}{3x^2+4}\\\\ f(x)=\dfrac{(4-3x^2)(4+3x^2)}{3x^2+4}\\\\ f(x)=4-3x^2$

Entonces:

$f(x)=4-3x^2\\\\ f'(x)=(4-3x^2)'\\\\ f'(x)=(4)'-(3x^2)'\\\\ f'(x)=(4)'-3(x^2)'\\\\ f'(x)=0-3\cdot2x\\\\ \boxed{f'(x)=-6x}$