Segunda Derivada

Segunda derivada

(%i81)

f(x):=(x**2+5)**3;

\[\mathrm{\tt (\%o81) }\quad \mathrm{f}\left( x\right) :={{\left( {{x}^{2}}+5\right) }^{3}}\]

(%i82)

'diff('f(x),x,2)=diff(f(x),x,2);

\[\mathrm{\tt (\%o82) }\quad \frac{{{d}^{2}}}{d\,{{x}^{2}}}\cdot \mathrm{f}\left( x\right) =6\cdot {{\left( {{x}^{2}}+5\right) }^{2}}+24\cdot {{x}^{2}}\cdot \left( {{x}^{2}}+5\right) \]

se puede simplificar agregando $ratsimp$

(%i83)

'diff('f(x),x,2)=diff(f(x),x,2),ratsimp;

\[\mathrm{\tt (\%o83) }\quad \frac{{{d}^{2}}}{d\,{{x}^{2}}}\cdot \mathrm{f}\left( x\right) =30\cdot {{x}^{4}}+180\cdot {{x}^{2}}+150\]

Tercera derivada

(%i84)

'diff('f(x),x,3)=diff(f(x),x,3),ratsimp;

\[\mathrm{\tt (\%o84) }\quad \frac{{{d}^{3}}}{d\,{{x}^{3}}}\cdot \mathrm{f}\left( x\right) =120\cdot {{x}^{3}}+360\cdot x\]