Calcular a derivada da função dada
11 set 2017, 00:49
Calcule (passo a passo) a derivada da função a seguir:
GABARITO: \(f'(x)=2x^5-4x^{3}+\frac{4x}{3}+\frac{1}{3}+\frac{1}{3x^{2}}\)
\(f(x)=\frac{1}{3}(x^{5}-2x^{3}+1)\cdot (x-\frac{1}{x})\)
GABARITO: \(f'(x)=2x^5-4x^{3}+\frac{4x}{3}+\frac{1}{3}+\frac{1}{3x^{2}}\)
\(f(x)=\frac{1}{3}(x^{5}-2x^{3}+1)\cdot (x-\frac{1}{x})\)
Re: Calcular a derivada da função dada [resolvida]
11 set 2017, 17:52
\(f(x)=\frac{1}{3}(x^5-2x^3+1)(x-\frac{1}{x})\)
\(f(x)=(\frac{x^5}{3}-\frac{2x^3}{3}+\frac{1}{3})(x-\frac{1}{x})\)
\(f(x)=\frac{x^6}{3}-\frac{x^5}{3x}-\frac{2x^4}{3}+\frac{2x^3}{3x}+\frac{x}{3}-\frac{1}{3x}\)
\(f(x)=\frac{x^6}{3}-(\frac{x^4}{3}+\frac{2x^4}{3})+\frac{2x^2}{3}+\frac{x}{3}-\frac{1}{3x}\)
\(f(x)=\frac{x^6}{3}-x^4+\frac{2x^2}{3}+\frac{x}{3}-\frac{x^{-1}}{3}\)
\(f'(x)=\frac{6x^5}{3}-4x^3+\frac{4x}{3}+\frac{1}{3}+\frac{x^{-2}}{3}\)
\(f'(x)=2x^5-4x^3+\frac{4x}{3}+\frac{1}{3}+\frac{1}{3x^2}\)
\(f(x)=(\frac{x^5}{3}-\frac{2x^3}{3}+\frac{1}{3})(x-\frac{1}{x})\)
\(f(x)=\frac{x^6}{3}-\frac{x^5}{3x}-\frac{2x^4}{3}+\frac{2x^3}{3x}+\frac{x}{3}-\frac{1}{3x}\)
\(f(x)=\frac{x^6}{3}-(\frac{x^4}{3}+\frac{2x^4}{3})+\frac{2x^2}{3}+\frac{x}{3}-\frac{1}{3x}\)
\(f(x)=\frac{x^6}{3}-x^4+\frac{2x^2}{3}+\frac{x}{3}-\frac{x^{-1}}{3}\)
\(f'(x)=\frac{6x^5}{3}-4x^3+\frac{4x}{3}+\frac{1}{3}+\frac{x^{-2}}{3}\)
\(f'(x)=2x^5-4x^3+\frac{4x}{3}+\frac{1}{3}+\frac{1}{3x^2}\)