Question

Determine o valor da derivada da função f(x) = 5x^3-2x^2+6x-7, para o ponto x = 3

Answer 1

Para a derivada daremos o tombo no expoente ... 

$f(x)\ =\ 5x^{3}\ -2x^{2}\ +\ 6x\ -\ 7 \\\\\\f(x)'\ =\ 3.5x^{3-1}\ -\ 2.2x^{2-1}\ +\ 1.6x^{1-1}\\\\\\f(x)'\ =\ 15x^{2}\ -\ 4x^{1}\ +\ 6x^{0}\\\\\\\boxed{f(x)'\ =\ 15x^{2}\ -\ 4x\ +\ 6 }\\\\\\\\\\Substituindo\ x\ por\ 3\ ...\\\\\\\\f(3)'\ =\ 15.3^{2}\ -\ 4.3\ +\ 6\\\\\\f(3)'\ =\ 15.9\ -\ 12\ +\ 6\\\\\\f(3)'\ =\ 135\ -\ 6\\\\\\\boxed{\boxed{f(3)'\ =\ 129\ }}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ok$