Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
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¿Cómo usar?
- Derivada de:
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Derivada de 1/(x+1)^2
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Derivada de (x+3)/(x-2)
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Derivada de (x+4)^2*(x+1)+9
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Derivada de e^(2-x)
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Expresiones idénticas
- y=arctan^ tres *sqrt*sin*x
- y es igual a arc tangente de al cubo multiplicar por raíz cuadrada de multiplicar por seno de multiplicar por x
- y es igual a arc tangente de en el grado tres multiplicar por raíz cuadrada de multiplicar por seno de multiplicar por x
- y=arctan^3*√*sin*x
- y=arctan3*sqrt*sin*x
- y=arctan³*sqrt*sin*x
- y=arctan en el grado 3*sqrt*sin*x
- y=arctan^3sqrtsinx
- y=arctan3sqrtsinx
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Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x)^2-2*x
- sqrt(x-1)/(sqrt(x^2)-x-1)
- sqrt(x)/(x+1)
- sqrt(x²+3x)
- sqrt(x^2+3)
- Seno sin
- sin(sin(x))
- sin^2*2x
- sin(x/5)
- sin(8*x)
- sin²(x)
Derivada de y=arctan^3*sqrt*sin*x
Solución
Ha introducido
[src]
3 ___ atan (x)*\/ x *sin(x)
$$\sqrt{x} \operatorname{atan}^{3}{\left(x \right)} \sin{\left(x \right)}$$
(atan(x)^3*sqrt(x))*sin(x)
Primera derivada
[src]
/ 3 ___ 2 \ |atan (x) 3*\/ x *atan (x)| ___ 3 |-------- + ----------------|*sin(x) + \/ x *atan (x)*cos(x) | ___ 2 | \2*\/ x 1 + x /
$$\sqrt{x} \cos{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)} + \left(\frac{3 \sqrt{x} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}^{3}{\left(x \right)}}{2 \sqrt{x}}\right) \sin{\left(x \right)}$$
Segunda derivada
[src]
/ / 2 ___ \ \ | |atan (x) 12*atan(x) 24*\/ x *(-1 + x*atan(x))| | | |-------- - -------------- + -------------------------|*sin(x) | | | 3/2 ___ / 2\ 2 | | | | x \/ x *\1 + x / / 2\ | / ___\ | | \ \1 + x / / |atan(x) 6*\/ x | ___ 2 | |- -------------------------------------------------------------- + |------- + -------|*atan(x)*cos(x) - \/ x *atan (x)*sin(x)|*atan(x) | 4 | ___ 2| | \ \ \/ x 1 + x / /
$$\left(- \sqrt{x} \sin{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)} + \left(\frac{6 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right) \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} - \frac{\left(\frac{24 \sqrt{x} \left(x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{12 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}}}\right) \sin{\left(x \right)}}{4}\right) \operatorname{atan}{\left(x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \
| ___ | 1 2 6*x*atan(x) 4*x *atan (x)| |
| 16*\/ x *|------ - atan (x) - ----------- + -------------| |
| 3 2 | 2 2 2 | | / 2 ___ \
|atan (x) 6*atan (x) \1 + x 1 + x 1 + x / 24*(-1 + x*atan(x))*atan(x)| / ___\ |atan (x) 12*atan(x) 24*\/ x *(-1 + x*atan(x))|
3*|-------- - ------------- + ---------------------------------------------------------- - ---------------------------|*sin(x) 2 |atan(x) 6*\/ x | 3*|-------- - -------------- + -------------------------|*atan(x)*cos(x)
| 5/2 3/2 / 2\ 2 2 | 3*atan (x)*|------- + -------|*sin(x) | 3/2 ___ / 2\ 2 |
| x x *\1 + x / / 2\ ___ / 2\ | | ___ 2| | x \/ x *\1 + x / / 2\ |
\ \1 + x / \/ x *\1 + x / / ___ 3 \ \/ x 1 + x / \ \1 + x / /
------------------------------------------------------------------------------------------------------------------------------ - \/ x *atan (x)*cos(x) - ------------------------------------- - ------------------------------------------------------------------------
8 2 4
$$- \sqrt{x} \cos{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)} - \frac{3 \left(\frac{6 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right) \sin{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)}}{2} - \frac{3 \left(\frac{24 \sqrt{x} \left(x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{12 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}}}\right) \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{4} + \frac{3 \left(\frac{16 \sqrt{x} \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{24 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{3}{\left(x \right)}}{x^{\frac{5}{2}}}\right) \sin{\left(x \right)}}{8}$$
Gráfico