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+3)
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Derivada de 4*y
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Derivada de (-1)/x-3*x
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Derivada de y=csc(3x²+1)
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Expresiones idénticas
- y=arctg^ tres *ln*sqrtx/x+ dos
- y es igual a arctg al cubo multiplicar por ln multiplicar por raíz cuadrada de x dividir por x más 2
- y es igual a arctg en el grado tres multiplicar por ln multiplicar por raíz cuadrada de x dividir por x más dos
- y=arctg^3*ln*√x/x+2
- y=arctg3*ln*sqrtx/x+2
- y=arctg³*ln*sqrtx/x+2
- y=arctg en el grado 3*ln*sqrtx/x+2
- y=arctg^3lnsqrtx/x+2
- y=arctg3lnsqrtx/x+2
- y=arctg^3*ln*sqrtx dividir por x+2
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Expresiones semejantes
- y=arctg^3*ln*sqrtx/x-2
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Expresiones con funciones
- ln
- ln(x+10)^11
- ln((x^2)-1)
- ln3x^5
- ln^3(x^2+1)
- ln(1+|x|)
Derivada de y=arctg^3*ln*sqrtx/x+2
Solución
Ha introducido
[src]
3 / 2\
atan (x)*log\x /*t*x
-------------------- + 2
x
$$2 + \frac{x t \log{\left(x^{2} \right)} \operatorname{atan}^{3}{\left(x \right)}}{x}$$
(((atan(x)^3*log(x^2))*t)*x)/x + 2
Primera derivada
[src]
/ 3 2 / 2\\
3 / 2\ |2*atan (x) 3*atan (x)*log\x /|
atan (x)*log\x /*t + t*x*|---------- + ------------------|
| x 2 | 3 / 2\
\ 1 + x / t*atan (x)*log\x /
---------------------------------------------------------- - ------------------
x x
$$- \frac{t \log{\left(x^{2} \right)} \operatorname{atan}^{3}{\left(x \right)}}{x} + \frac{t x \left(\frac{3 \log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}^{3}{\left(x \right)}}{x}\right) + t \log{\left(x^{2} \right)} \operatorname{atan}^{3}{\left(x \right)}}{x}$$
Segunda derivada
[src]
/ / / / 2\\ \ \
| | |2*atan(x) 3*log\x /| / 2\| |
| |x*|--------- + ---------| + atan(x)*log\x /|*atan(x) |
| / 2 / 2\ / 2\\ 2 / / 2\\ 2 / 2\ | | x 2 | | / 2\|
| |atan (x) 3*log\x / 6*atan(x) 3*x*atan(x)*log\x /| 2*atan (x) |2*atan(x) 3*log\x /| atan (x)*log\x / \ \ 1 + x / / 3*atan(x)*log\x /|
t*|- 2*x*|-------- - --------- - ---------- + -------------------| - ---------- + 2*|--------- + ---------|*atan(x) + ---------------- - ----------------------------------------------------- - -----------------|*atan(x)
| | 2 2 / 2\ 2 | x | x 2 | x x 2 |
| | x / 2\ x*\1 + x / / 2\ | \ 1 + x / 1 + x |
\ \ \1 + x / \1 + x / / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
$$\frac{t \left(- 2 x \left(\frac{3 x \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{3 \log{\left(x^{2} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right) + 2 \left(\frac{3 \log{\left(x^{2} \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}{\left(x \right)}}{x}\right) \operatorname{atan}{\left(x \right)} - \frac{3 \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \frac{\left(x \left(\frac{3 \log{\left(x^{2} \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}{\left(x \right)}}{x}\right) + \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}}{x} + \frac{\log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{x} - \frac{2 \operatorname{atan}^{2}{\left(x \right)}}{x}\right) \operatorname{atan}{\left(x \right)}}{x}$$
Tercera derivada
[src]
/ / 2 3 / 2\ 2 2 / 2\ / 2\ 2 2 / 2\\ / 2 / 2\ / 2\\ / / 2 / 2\ / 2\\ / / 2\\ \ \
| | 18*atan (x) 2*atan (x) 3*log\x / 9*atan (x) 3*atan (x)*log\x / 18*atan(x) 18*x*atan(x)*log\x / 12*x *atan (x)*log\x /| |atan (x) 3*log\x / 6*atan(x) 3*x*atan(x)*log\x /| / / / 2\\ \ | |atan (x) 3*log\x / 6*atan(x) 3*x*atan(x)*log\x /| |2*atan(x) 3*log\x /| | |
|x*|- ----------- + ---------- + --------- - ----------- - ------------------ + ----------- - -------------------- + ----------------------| - 3*|-------- - --------- - ---------- + -------------------|*atan(x) 2 | |2*atan(x) 3*log\x /| / 2\| 2*|x*|-------- - --------- - ---------- + -------------------| - |--------- + ---------|*atan(x)|*atan(x) |
| | 2 3 3 2 / 2\ 2 2 3 3 | | 2 2 / 2\ 2 | atan (x)*|x*|--------- + ---------| + atan(x)*log\x /| | | 2 2 / 2\ 2 | | x 2 | | |
| | / 2\ x / 2\ x *\1 + x / / 2\ / 2\ / 2\ / 2\ | | x / 2\ x*\1 + x / / 2\ | 3 | | x 2 | | 3 / 2\ 2 | | x / 2\ x*\1 + x / / 2\ | \ 1 + x / | 2 / 2\ / 2\ 2 / 2\|
| \ \1 + x / \1 + x / \1 + x / x*\1 + x / \1 + x / \1 + x / / \ \1 + x / \1 + x / / 3*atan (x) \ \ 1 + x / / atan (x)*log\x / 6*atan (x) \ \ \1 + x / \1 + x / / / 3*atan (x)*log\x / 3*atan(x)*log\x / 3*atan (x)*log\x /|
2*t*|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------- + ------------------------------------------------------ - ---------------- - ----------- + --------------------------------------------------------------------------------------------------------- + ------------------ - ----------------- + ------------------|
| x 3 3 3 2 / 2\ 2 2 2 2 / 2\ |
| x x x x *\1 + x / x / 2\ / 2\ x *\1 + x / |
\ \1 + x / x*\1 + x / /
$$2 t \left(\frac{3 \log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{x \left(\frac{12 x^{2} \log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{18 x \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{3 \log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{18 \operatorname{atan}^{2}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{3 \log{\left(x^{2} \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{18 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)^{2}} - \frac{9 \operatorname{atan}^{2}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} + \frac{2 \operatorname{atan}^{3}{\left(x \right)}}{x^{3}}\right) - 3 \left(\frac{3 x \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{3 \log{\left(x^{2} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right) \operatorname{atan}{\left(x \right)}}{x} - \frac{3 \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)^{2}} + \frac{2 \left(x \left(\frac{3 x \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{3 \log{\left(x^{2} \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}{\left(x \right)}}{x \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{2}}\right) - \left(\frac{3 \log{\left(x^{2} \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}{\left(x \right)}}{x}\right) \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}}{x^{2}} + \frac{3 \log{\left(x^{2} \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} - \frac{6 \operatorname{atan}^{2}{\left(x \right)}}{x^{2} \left(x^{2} + 1\right)} + \frac{\left(x \left(\frac{3 \log{\left(x^{2} \right)}}{x^{2} + 1} + \frac{2 \operatorname{atan}{\left(x \right)}}{x}\right) + \log{\left(x^{2} \right)} \operatorname{atan}{\left(x \right)}\right) \operatorname{atan}^{2}{\left(x \right)}}{x^{3}} - \frac{\log{\left(x^{2} \right)} \operatorname{atan}^{3}{\left(x \right)}}{x^{3}} + \frac{3 \operatorname{atan}^{3}{\left(x \right)}}{x^{3}}\right)$$