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 e^x*sin(x)
-
Derivada de x*e^(1/x)
- Derivada de x!
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Derivada de e^y
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Expresiones idénticas
- z=arctg*(ln*(x^ dos +x- tres))/x
- z es igual a arctg multiplicar por (ln multiplicar por (x al cuadrado más x menos 3)) dividir por x
- z es igual a arctg multiplicar por (ln multiplicar por (x en el grado dos más x menos tres)) dividir por x
- z=arctg*(ln*(x2+x-3))/x
- z=arctg*ln*x2+x-3/x
- z=arctg*(ln*(x²+x-3))/x
- z=arctg*(ln*(x en el grado 2+x-3))/x
- z=arctg(ln(x^2+x-3))/x
- z=arctg(ln(x2+x-3))/x
- z=arctglnx2+x-3/x
- z=arctglnx^2+x-3/x
- z=arctg*(ln*(x^2+x-3)) dividir por x
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Expresiones semejantes
- z=arctg*(ln*(x^2-x-3))/x
- z=arctg*(ln*(x^2+x+3))/x
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Expresiones con funciones
- arctg
- arctg(sqrt(x))
- arctg^2(1/x)
- arctg(cos(x))
- arctg(x+cosx)
- ln
- ln(x+√(x²+1))
- ln(x-4)
- ln(x²+2x)
- ln(x^2+2x)
- ln((x+1)÷(x-1))
Derivada de z=arctg*(ln*(x^2+x-3))/x
Solución
Ha introducido
[src]
/ / 2 \\
atan\log\x + x - 3//
---------------------
x
$$\frac{\operatorname{atan}{\left(\log{\left(\left(x^{2} + x\right) - 3 \right)} \right)}}{x}$$
atan(log(x^2 + x - 3))/x
Primera derivada
[src]
/ / 2 \\
atan\log\x + x - 3// 1 + 2*x
- --------------------- + -------------------------------------
2 / 2/ 2 \\ / 2 \
x x*\1 + log \x + x - 3//*\x + x - 3/
$$\frac{2 x + 1}{x \left(\left(x^{2} + x\right) - 3\right) \left(\log{\left(\left(x^{2} + x\right) - 3 \right)}^{2} + 1\right)} - \frac{\operatorname{atan}{\left(\log{\left(\left(x^{2} + x\right) - 3 \right)} \right)}}{x^{2}}$$
Segunda derivada
[src]
2 2 / 2\
(1 + 2*x) 2*(1 + 2*x) *log\-3 + x + x /
-2 + ----------- + -------------------------------------
/ / 2\\ 2 / 2/ 2\\ / 2\
2*atan\log\-3 + x + x // -3 + x + x \1 + log \-3 + x + x //*\-3 + x + x / 2*(1 + 2*x)
------------------------ - -------------------------------------------------------- - ---------------------------------------
2 / 2/ 2\\ / 2\ / 2/ 2\\ / 2\
x \1 + log \-3 + x + x //*\-3 + x + x / x*\1 + log \-3 + x + x //*\-3 + x + x /
-----------------------------------------------------------------------------------------------------------------------------
x
$$\frac{- \frac{\frac{\left(2 x + 1\right)^{2}}{x^{2} + x - 3} + \frac{2 \left(2 x + 1\right)^{2} \log{\left(x^{2} + x - 3 \right)}}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} - 2}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} - \frac{2 \left(2 x + 1\right)}{x \left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} + \frac{2 \operatorname{atan}{\left(\log{\left(x^{2} + x - 3 \right)} \right)}}{x^{2}}}{x}$$
Tercera derivada
[src]
/ 2 / 2\ 2 2 / 2\ 2 2/ 2\ \
| (1 + 2*x) 6*log\-3 + x + x / (1 + 2*x) 3*(1 + 2*x) *log\-3 + x + x / 4*(1 + 2*x) *log \-3 + x + x / | / 2 2 / 2\ \
2*(1 + 2*x)*|-3 + ----------- - --------------------- - ------------------------------------- + ------------------------------------- + --------------------------------------| | (1 + 2*x) 2*(1 + 2*x) *log\-3 + x + x / |
| 2 2/ 2\ / 2/ 2\\ / 2\ / 2/ 2\\ / 2\ 2 | 3*|-2 + ----------- + -------------------------------------|
/ / 2\\ | -3 + x + x 1 + log \-3 + x + x / \1 + log \-3 + x + x //*\-3 + x + x / \1 + log \-3 + x + x //*\-3 + x + x / / 2/ 2\\ / 2\| | 2 / 2/ 2\\ / 2\|
6*atan\log\-3 + x + x // \ \1 + log \-3 + x + x // *\-3 + x + x // \ -3 + x + x \1 + log \-3 + x + x //*\-3 + x + x // 6*(1 + 2*x)
- ------------------------ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------ + ----------------------------------------
3 2 / 2/ 2\\ / 2\ 2 / 2/ 2\\ / 2\
x / 2/ 2\\ / 2\ x*\1 + log \-3 + x + x //*\-3 + x + x / x *\1 + log \-3 + x + x //*\-3 + x + x /
\1 + log \-3 + x + x //*\-3 + x + x /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
x
$$\frac{\frac{2 \left(2 x + 1\right) \left(\frac{\left(2 x + 1\right)^{2}}{x^{2} + x - 3} + \frac{3 \left(2 x + 1\right)^{2} \log{\left(x^{2} + x - 3 \right)}}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} - \frac{\left(2 x + 1\right)^{2}}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} + \frac{4 \left(2 x + 1\right)^{2} \log{\left(x^{2} + x - 3 \right)}^{2}}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right)^{2} \left(x^{2} + x - 3\right)} - 3 - \frac{6 \log{\left(x^{2} + x - 3 \right)}}{\log{\left(x^{2} + x - 3 \right)}^{2} + 1}\right)}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)^{2}} + \frac{3 \left(\frac{\left(2 x + 1\right)^{2}}{x^{2} + x - 3} + \frac{2 \left(2 x + 1\right)^{2} \log{\left(x^{2} + x - 3 \right)}}{\left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} - 2\right)}{x \left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} + \frac{6 \left(2 x + 1\right)}{x^{2} \left(\log{\left(x^{2} + x - 3 \right)}^{2} + 1\right) \left(x^{2} + x - 3\right)} - \frac{6 \operatorname{atan}{\left(\log{\left(x^{2} + x - 3 \right)} \right)}}{x^{3}}}{x}$$
Gráfico