Sr Examen

Otras calculadoras

y=tg^2(arcsinx-x)
Derivada de la función/ arcsin/ y=tg^2/ y=tg^2(arcsinx-x)

Derivada de y=tg^2(arcsinx-x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   2             
tan (asin(x) - x)
tan⁡2(−x+asin⁡(x))\tan^{2}{\left(- x + \operatorname{asin}{\left(x \right)} \right)} 
tan(asin(x) - x)^2
Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  /       2             \ /          1     \                 
2*\1 + tan (asin(x) - x)/*|-1 + -----------|*tan(asin(x) - x)
                          |        ________|                 
                          |       /      2 |                 
                          \     \/  1 - x  /
2(−1+11−x2)(tan⁡2(−x+asin⁡(x))+1)tan⁡(−x+asin⁡(x))2 \left(-1 + \frac{1}{\sqrt{1 - x^{2}}}\right) \left(\tan^{2}{\left(- x + \operatorname{asin}{\left(x \right)} \right)} + 1\right) \tan{\left(- x + \operatorname{asin}{\left(x \right)} \right)}
Simplificar
Segunda derivada [src] 
                          /                 2                                              2                                       \
  /       2             \ |/         1     \  /       2             \     /         1     \     2                x*tan(x - asin(x))|
2*\1 + tan (x - asin(x))/*||1 - -----------| *\1 + tan (x - asin(x))/ + 2*|1 - -----------| *tan (x - asin(x)) - ------------------|
                          ||       ________|                              |       ________|                                 3/2    |
                          ||      /      2 |                              |      /      2 |                         /     2\       |
                          \\    \/  1 - x  /                              \    \/  1 - x  /                         \1 - x /       /
2(tan⁡2(x−asin⁡(x))+1)(−xtan⁡(x−asin⁡(x))(1−x2)32+(1−11−x2)2(tan⁡2(x−asin⁡(x))+1)+2(1−11−x2)2tan⁡2(x−asin⁡(x)))2 \left(\tan^{2}{\left(x - \operatorname{asin}{\left(x \right)} \right)} + 1\right) \left(- \frac{x \tan{\left(x - \operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{2} \left(\tan^{2}{\left(x - \operatorname{asin}{\left(x \right)} \right)} + 1\right) + 2 \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{2} \tan^{2}{\left(x - \operatorname{asin}{\left(x \right)} \right)}\right)
Simplificar
Tercera derivada [src] 
                          /                                                                                                                                                             2              /         1     \       /       2             \ /         1     \\
                          |                                                                                                                                                      6*x*tan (x - asin(x))*|1 - -----------|   3*x*\1 + tan (x - asin(x))/*|1 - -----------||
                          |                                                                                                                                                                            |       ________|                               |       ________||
                          |                                        3                        2                                       3                                                                  |      /      2 |                               |      /      2 ||
  /       2             \ |  tan(x - asin(x))     /         1     \     3                3*x *tan(x - asin(x))     /         1     \  /       2             \                                          \    \/  1 - x  /                               \    \/  1 - x  /|
2*\1 + tan (x - asin(x))/*|- ---------------- + 4*|1 - -----------| *tan (x - asin(x)) - --------------------- + 8*|1 - -----------| *\1 + tan (x - asin(x))/*tan(x - asin(x)) - --------------------------------------- - ---------------------------------------------|
                          |            3/2        |       ________|                                   5/2          |       ________|                                                                   3/2                                          3/2                 |
                          |    /     2\           |      /      2 |                           /     2\             |      /      2 |                                                           /     2\                                     /     2\                    |
                          \    \1 - x /           \    \/  1 - x  /                           \1 - x /             \    \/  1 - x  /                                                           \1 - x /                                     \1 - x /                    /
2(tan⁡2(x−asin⁡(x))+1)(−3x2tan⁡(x−asin⁡(x))(1−x2)52−3x(1−11−x2)(tan⁡2(x−asin⁡(x))+1)(1−x2)32−6x(1−11−x2)tan⁡2(x−asin⁡(x))(1−x2)32+8(1−11−x2)3(tan⁡2(x−asin⁡(x))+1)tan⁡(x−asin⁡(x))+4(1−11−x2)3tan⁡3(x−asin⁡(x))−tan⁡(x−asin⁡(x))(1−x2)32)2 \left(\tan^{2}{\left(x - \operatorname{asin}{\left(x \right)} \right)} + 1\right) \left(- \frac{3 x^{2} \tan{\left(x - \operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{3 x \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right) \left(\tan^{2}{\left(x - \operatorname{asin}{\left(x \right)} \right)} + 1\right)}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6 x \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right) \tan^{2}{\left(x - \operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 8 \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{3} \left(\tan^{2}{\left(x - \operatorname{asin}{\left(x \right)} \right)} + 1\right) \tan{\left(x - \operatorname{asin}{\left(x \right)} \right)} + 4 \left(1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{3} \tan^{3}{\left(x - \operatorname{asin}{\left(x \right)} \right)} - \frac{\tan{\left(x - \operatorname{asin}{\left(x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)
Simplificar
Gráfico
Derivada de y=tg^2(arcsinx-x)
    © Sr Examen – Калькулятор