Question

Encontre a derivada da função y=(x³-7x).(x²-7)

Answer 1

$f(x)=u(x)\cdotv(x)\to f'(x)=u'(x)\cdot v(x)+u(x)\cdot v'(x)\\\\\\u(x)=x^3-7x\\\\u'(x)=3x^2-7\\\\v(x)=x^2-7\\\\v'(x)=2x\\\\\\y'=(3x^2-7)(x^2-7)+(x^3-7x)(2x)\\\\y'=3x^5-21x^2-7x^2+49+2x^4-7x^2\\\\\boxed{y'=3x^5+2x^4-35x^2+49}$