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y=arctg(lnx)+ln(sinx)
Derivada de la función/ arctg/ (sinx)/ y=arctg(lnx)+ln(sinx)

Derivada de y=arctg(lnx)+ln(sinx)

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

Gráfico:

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Solución

Ha introducido [src] 
atan(log(x)) + log(sin(x))
log⁡(sin⁡(x))+atan⁡(log⁡(x))\log{\left(\sin{\left(x \right)} \right)} + \operatorname{atan}{\left(\log{\left(x \right)} \right)} 
atan(log(x)) + log(sin(x))
Gráfica
02468-8-6-4-2-1010-100100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       1          cos(x)
--------------- + ------
  /       2   \   sin(x)
x*\1 + log (x)/
cos⁡(x)sin⁡(x)+1x(log⁡(x)2+1)\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}
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Segunda derivada [src] 
 /                          2                       \
 |           1           cos (x)        2*log(x)    |
-|1 + ---------------- + ------- + -----------------|
 |     2 /       2   \      2                      2|
 |    x *\1 + log (x)/   sin (x)    2 /       2   \ |
 \                                 x *\1 + log (x)/ /
−(1+cos⁡2(x)sin⁡2(x)+1x2(log⁡(x)2+1)+2log⁡(x)x2(log⁡(x)2+1)2)- (1 + \frac{\cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{1}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{2 \log{\left(x \right)}}{x^{2} \left(\log{\left(x \right)}^{2} + 1\right)^{2}})
Simplificar
Tercera derivada [src] 
  /                      3                                                                2       \
  |       1           cos (x)   cos(x)           1                3*log(x)           4*log (x)    |
2*|---------------- + ------- + ------ - ----------------- + ----------------- + -----------------|
  | 3 /       2   \      3      sin(x)                   2                   2                   3|
  |x *\1 + log (x)/   sin (x)             3 /       2   \     3 /       2   \     3 /       2   \ |
  \                                      x *\1 + log (x)/    x *\1 + log (x)/    x *\1 + log (x)/ /
2(cos⁡(x)sin⁡(x)+cos⁡3(x)sin⁡3(x)+1x3(log⁡(x)2+1)+3log⁡(x)x3(log⁡(x)2+1)2−1x3(log⁡(x)2+1)2+4log⁡(x)2x3(log⁡(x)2+1)3)2 \left(\frac{\cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{\cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} + \frac{1}{x^{3} \left(\log{\left(x \right)}^{2} + 1\right)} + \frac{3 \log{\left(x \right)}}{x^{3} \left(\log{\left(x \right)}^{2} + 1\right)^{2}} - \frac{1}{x^{3} \left(\log{\left(x \right)}^{2} + 1\right)^{2}} + \frac{4 \log{\left(x \right)}^{2}}{x^{3} \left(\log{\left(x \right)}^{2} + 1\right)^{3}}\right)
Simplificar
Gráfico
Derivada de y=arctg(lnx)+ln(sinx)
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