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- 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
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- Derivada de:
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Derivada de 2^(3*x)
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Derivada de 6/x
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Derivada de x^10
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Derivada de -2/x
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Expresiones idénticas
- y=arctg^3sqrt(x)/x+ cuatro
- y es igual a arctg al cubo raíz cuadrada de (x) dividir por x más 4
- y es igual a arctg al cubo raíz cuadrada de (x) dividir por x más cuatro
- y=arctg^3√(x)/x+4
- y=arctg3sqrt(x)/x+4
- y=arctg3sqrtx/x+4
- y=arctg³sqrt(x)/x+4
- y=arctg en el grado 3sqrt(x)/x+4
- y=arctg^3sqrtx/x+4
- y=arctg^3sqrt(x) dividir por x+4
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Expresiones semejantes
- y=arctg^3sqrt(x)/x-4
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Expresiones con funciones
- arctg
- arctg(x)
- arctg3x
- arctg5x
- arctg√(x-1)
- arctgln5x
Derivada de y=arctg^3sqrt(x)/x+4
Solución
Ha introducido
[src]
3 ___
atan (x)*\/ x
-------------- + 4
x
$$4 + \frac{\sqrt{x} \operatorname{atan}^{3}{\left(x \right)}}{x}$$
(atan(x)^3*sqrt(x))/x + 4
Primera derivada
[src]
3 ___ 2
atan (x) 3*\/ x *atan (x)
-------- + ----------------
___ 2 3
2*\/ x 1 + x atan (x)
--------------------------- - --------
x 3/2
x
$$\frac{\frac{3 \sqrt{x} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}^{3}{\left(x \right)}}{2 \sqrt{x}}}{x} - \frac{\operatorname{atan}^{3}{\left(x \right)}}{x^{\frac{3}{2}}}$$
Segunda derivada
[src]
/ 2 ___ 3/2 \ | atan (x) 24*\/ x 12*atan(x) 24*x *atan(x) / ___\ | | -------- - --------- - -------------- + --------------- |atan(x) 6*\/ x | | | 3/2 2 ___ / 2\ 2 |------- + -------|*atan(x)| | x / 2\ \/ x *\1 + x / / 2\ 2 | ___ 2| | | \1 + x / \1 + x / 3*atan (x) 3*atan(x) \ \/ x 1 + x / | |- ------------------------------------------------------- + ---------- - ------------- - ---------------------------|*atan(x) | 4*x 5/2 3/2 / 2\ 2 | \ 2*x x *\1 + x / 2*x /
$$\left(- \frac{\frac{24 x^{\frac{3}{2}} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{24 \sqrt{x}}{\left(x^{2} + 1\right)^{2}} - \frac{12 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}}}}{4 x} - \frac{\left(\frac{6 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right) \operatorname{atan}{\left(x \right)}}{2 x^{2}} - \frac{3 \operatorname{atan}{\left(x \right)}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{3 \operatorname{atan}^{2}{\left(x \right)}}{2 x^{\frac{5}{2}}}\right) \operatorname{atan}{\left(x \right)}$$
Tercera derivada
[src]
/ 3 ___ 3/2 ___ 2 2 5/2 2 \ / 2 ___ 3/2 \
|atan (x) 16*\/ x 96*x *atan(x) 40*\/ x *atan (x) 6*atan (x) 24*atan(x) 64*x *atan (x)| / ___\ |atan (x) 24*\/ x 12*atan(x) 24*x *atan(x)|
3*|-------- + --------- - --------------- - ----------------- - ------------- + --------------- + ----------------| 2 |atan(x) 6*\/ x | |-------- - --------- - -------------- + ---------------|*atan(x)
| 5/2 3 3 2 3/2 / 2\ 2 3 | atan (x)*|------- + -------| | 3/2 2 ___ / 2\ 2 |
3 | x / 2\ / 2\ / 2\ x *\1 + x / ___ / 2\ / 2\ | | ___ 2| | x / 2\ \/ x *\1 + x / / 2\ | 2 2
15*atan (x) \ \1 + x / \1 + x / \1 + x / \/ x *\1 + x / \1 + x / / \ \/ x 1 + x / \ \1 + x / \1 + x / / 6*atan(x) 6*atan (x) 9*atan (x)
- ----------- + ------------------------------------------------------------------------------------------------------------------- + ---------------------------- + ----------------------------------------------------------------- - -------------- + --------------- + -------------
7/2 8*x 3 2 2 2 5/2 / 2\
4*x x 2*x 3/2 / 2\ ___ / 2\ x *\1 + x /
x *\1 + x / \/ x *\1 + x /
$$\frac{3 \left(\frac{64 x^{\frac{5}{2}} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{96 x^{\frac{3}{2}} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{40 \sqrt{x} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{16 \sqrt{x}}{\left(x^{2} + 1\right)^{3}} + \frac{24 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{3}{\left(x \right)}}{x^{\frac{5}{2}}}\right)}{8 x} + \frac{\left(\frac{24 x^{\frac{3}{2}} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{24 \sqrt{x}}{\left(x^{2} + 1\right)^{2}} - \frac{12 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}}}\right) \operatorname{atan}{\left(x \right)}}{2 x^{2}} + \frac{\left(\frac{6 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{3}} + \frac{6 \operatorname{atan}^{2}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)^{2}} + \frac{9 \operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{5}{2}} \left(x^{2} + 1\right)} - \frac{15 \operatorname{atan}^{3}{\left(x \right)}}{4 x^{\frac{7}{2}}}$$
Gráfico