Sr Examen

Derivada de y=(cosx)^3x

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
   3     
cos (x)*x
$$x \cos^{3}{\left(x \right)}$$
cos(x)^3*x
Gráfica
Primera derivada [src]
   3             2          
cos (x) - 3*x*cos (x)*sin(x)
$$- 3 x \sin{\left(x \right)} \cos^{2}{\left(x \right)} + \cos^{3}{\left(x \right)}$$
Segunda derivada [src]
  /  /     2           2   \                  \       
3*\x*\- cos (x) + 2*sin (x)/ - 2*cos(x)*sin(x)/*cos(x)
$$3 \left(x \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) - 2 \sin{\left(x \right)} \cos{\left(x \right)}\right) \cos{\left(x \right)}$$
Tercera derivada [src]
  /  /     2           2   \            /       2           2   \       \
3*\3*\- cos (x) + 2*sin (x)/*cos(x) - x*\- 7*cos (x) + 2*sin (x)/*sin(x)/
$$3 \left(- x \left(2 \sin^{2}{\left(x \right)} - 7 \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} + 3 \left(2 \sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \cos{\left(x \right)}\right)$$
Gráfico
Derivada de y=(cosx)^3x