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y=arctg^2-lnsinx
Derivada de la función/ ctg^2/ arctg/ lnsinx/ y=arctg^2-lnsinx

Derivada de y=arctg^2-lnsinx

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    2                 
atan (x) - log(sin(x))
−log⁡(sin⁡(x))+atan⁡2(x)- \log{\left(\sin{\left(x \right)} \right)} + \operatorname{atan}^{2}{\left(x \right)} 
atan(x)^2 - log(sin(x))
Gráfica
02468-8-6-4-2-1010-200200
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  cos(x)   2*atan(x)
- ------ + ---------
  sin(x)          2 
             1 + x
−cos⁡(x)sin⁡(x)+2atan⁡(x)x2+1- \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 \operatorname{atan}{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
                   2                 
        2       cos (x)   4*x*atan(x)
1 + --------- + ------- - -----------
            2      2               2 
    /     2\    sin (x)    /     2\  
    \1 + x /               \1 + x /
−4xatan⁡(x)(x2+1)2+1+cos⁡2(x)sin⁡2(x)+2(x2+1)2- \frac{4 x \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + 1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{2}{\left(x^{2} + 1\right)^{2}}
Simplificar
Tercera derivada [src] 
  /     3                                          2        \
  |  cos (x)   cos(x)      6*x      2*atan(x)   8*x *atan(x)|
2*|- ------- - ------ - --------- - --------- + ------------|
  |     3      sin(x)           3           2            3  |
  |  sin (x)            /     2\    /     2\     /     2\   |
  \                     \1 + x /    \1 + x /     \1 + x /   /
2(8x2atan⁡(x)(x2+1)3−6x(x2+1)3−cos⁡(x)sin⁡(x)−cos⁡3(x)sin⁡3(x)−2atan⁡(x)(x2+1)2)2 \left(\frac{8 x^{2} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{6 x}{\left(x^{2} + 1\right)^{3}} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} - \frac{\cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - \frac{2 \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)
Simplificar
Gráfico
Derivada de y=arctg^2-lnsinx
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