Question

derivada do produto f(x)(x^-3+5^-4)(2x^3-5x^2)

Answer 1

$f(x)=uv\\f'(x)=u'v+v'u\\f(x)=(x^{-3}+5^{-4})(2x^3-5x^2)\\f'(x)=(-3x^{-4})(2x^3-5x^2)+(6x^2-10x)(x^{-3}+5^{-4})\\f'(x)=-6x^{-1}+15x^{-2}+6x^{-1}+(6\cdot5^{-4})x^2-10x^{-2}-(2\cdot5^{-3})\\f'(x)=\frac5{x^2}+0.0096x^2-0.016$