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
-
¿Cómo usar?
- Derivada de:
-
Derivada de 1/(x+3)
-
Derivada de 4*y
-
Derivada de (-1)/x-3*x
-
Derivada de y=csc(3x²+1)
-
Expresiones idénticas
- x^tgx(((tgx/x)-(uno /cos^ dos))(uno /lnx))
- x en el grado tgx(((tgx dividir por x) menos (1 dividir por coseno de al cuadrado ))(1 dividir por lnx))
- x en el grado tgx(((tgx dividir por x) menos (uno dividir por coseno de en el grado dos))(uno dividir por lnx))
- xtgx(((tgx/x)-(1/cos2))(1/lnx))
- xtgxtgx/x-1/cos21/lnx
- x^tgx(((tgx/x)-(1/cos²))(1/lnx))
- x en el grado tgx(((tgx/x)-(1/cos en el grado 2))(1/lnx))
- x^tgxtgx/x-1/cos^21/lnx
- x^tgx(((tgx dividir por x)-(1 dividir por cos^2))(1 dividir por lnx))
-
Expresiones semejantes
- x^tgx(((tgx/x)+(1/cos^2))(1/lnx))
-
Expresiones con funciones
- Coseno cos
- cos(log(x))+x^2*tan(x)
- cos(-6x+7)
- cos(3*x)/3
- cos(2*x+pi/3)
- cos(2-3*x)
Derivada de x^tgx(((tgx/x)-(1/cos^2))(1/lnx))
Solución
Ha introducido
[src]
tan(x) 1
------ - -------
x 2
tan(x) cos (x)
x *----------------
log(x)
$$x^{\tan{\left(x \right)}} \frac{- \frac{1}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x}}{\log{\left(x \right)}}$$
x^tan(x)*((tan(x)/x - 1/cos(x)^2)/log(x))
Primera derivada
[src]
/ 2 \
|1 + tan (x) tan(x) 2*sin(x) tan(x) 1 | tan(x) /tan(x) / 2 \ \ /tan(x) 1 \
|----------- - ------ - -------- ------ - -------| x *|------ + \1 + tan (x)/*log(x)|*|------ - -------|
| x 2 3 x 2 | \ x / | x 2 |
tan(x) | x cos (x) cos (x)| \ cos (x)/
x *|------------------------------- - ----------------| + ----------------------------------------------------------
| log(x) 2 | log(x)
\ x*log (x) /
$$\frac{x^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(- \frac{1}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x}\right)}{\log{\left(x \right)}} + x^{\tan{\left(x \right)}} \left(\frac{- \frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{\tan^{2}{\left(x \right)} + 1}{x} - \frac{\tan{\left(x \right)}}{x^{2}}}{\log{\left(x \right)}} - \frac{- \frac{1}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x}}{x \log{\left(x \right)}^{2}}\right)$$
Segunda derivada
[src]
/ / 2 \ \
| / 1 tan(x)\ |tan(x) 1 + tan (x) 2*sin(x)| / 2 \ / 1 tan(x)\|
| | - ------- + ------| 2*|------ - ----------- + --------| |1 + ------|*|------- - ------||
| / 2 / 2 \ \ / 2 \ | 2 2 x | 2 | 2 x 3 | / 2 \ \ log(x)/ | 2 x ||
tan(x) | 2 / 1 tan(x)\ |/tan(x) / 2 \ \ tan(x) 2*\1 + tan (x)/ / 2 \ | 2*tan(x) 2*\1 + tan (x)/ /tan(x) / 2 \ \ |tan(x) 1 + tan (x) 2*sin(x) cos (x) | 6*sin (x) \ x cos (x) / 2*\1 + tan (x)/*tan(x) \cos (x) /|
-x *|------- + |------- - ------|*||------ + \1 + tan (x)/*log(x)| - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| - -------- + --------------- + 2*|------ + \1 + tan (x)/*log(x)|*|------ - ----------- + -------- + ------------------| + --------- - ----------------------------------- - ---------------------- + -------------------------------|
| 2 | 2 x | |\ x / 2 x | 3 2 \ x / | 2 x 3 x*log(x) | 4 x*log(x) x 2 |
\cos (x) \cos (x) / \ x / x x \ x cos (x) / cos (x) x *log(x) /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(x)
$$- \frac{x^{\tan{\left(x \right)}} \left(2 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{- \frac{1}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x}}{x \log{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right) + \left(\frac{1}{\cos^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{x}\right) \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) + \frac{6 \sin^{2}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{2}{\cos^{2}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{2 \left(\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right)}{x \log{\left(x \right)}} + \frac{\left(1 + \frac{2}{\log{\left(x \right)}}\right) \left(\frac{1}{\cos^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{x}\right)}{x^{2} \log{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} - \frac{2 \tan{\left(x \right)}}{x^{3}}\right)}{\log{\left(x \right)}}$$
Tercera derivada
[src]
/ / / 2 \ \ / 2 2 / 2 \ \ / 2 \\
| | |tan(x) 1 + tan (x) 2*sin(x)| / 2 \ / 1 tan(x)\| / 1 tan(x)\ | 1 1 + tan (x) tan(x) 3*sin (x) \1 + tan (x)/*tan(x)| / 1 tan(x)\ / 3 3 \ / 2 \ |tan(x) 1 + tan (x) 2*sin(x)||
| 2 | 2*|------ - ----------- + --------| |1 + ------|*|------- - ------|| | - ------- + ------| 6*|------- + ----------- - ------ + --------- - --------------------| 2*|------- - ------|*|1 + ------ + -------| 3*|1 + ------|*|------ - ----------- + --------||
| / 3 / 2 \ 2 / / 2 \ \ / 2 \ \ / 2 \ / 2 \ | / 2 \ 2 | 2 x 3 | / 2 \ \ log(x)/ | 2 x || / 2 / 2 \ \ | 2 2 x | 3 | 2 2 3 4 x | 2 / 2 \ / 2 \ | 2 x | | log(x) 2 | \ log(x)/ | 2 x 3 ||
tan(x) |/ 1 tan(x)\ |/tan(x) / 2 \ \ 3*\1 + tan (x)/ 2*tan(x) / 2 \ /tan(x) / 2 \ \ | tan(x) 2*\1 + tan (x)/ / 2 \ | 2 / 2 \ 6*\1 + tan (x)/*tan(x)| 6*\1 + tan (x)/ 2*\1 + tan (x)/ /tan(x) / 2 \ \ | 2 2*tan(x) 2*\1 + tan (x)/ 6*sin (x) \ x cos (x) / 2*\1 + tan (x)/*tan(x) \cos (x) /| |/tan(x) / 2 \ \ tan(x) 2*\1 + tan (x)/ / 2 \ | |tan(x) 1 + tan (x) 2*sin(x) cos (x) | 6*tan(x) 16*sin(x) 24*sin (x) \cos (x) x x cos (x) / 4*tan (x)*\1 + tan (x)/ 6*\1 + tan (x)/*tan(x) \cos (x) / \ log (x)/ \ x cos (x) /|
-x *||------- - ------|*||------ + \1 + tan (x)/*log(x)| - --------------- + -------- + 2*\1 + tan (x)/ *log(x) + 3*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| + 4*tan (x)*\1 + tan (x)/*log(x) + ----------------------| - --------------- - ---------------- + 3*|------ + \1 + tan (x)/*log(x)|*|------- - -------- + --------------- + --------- - ----------------------------------- - ---------------------- + -------------------------------| + 3*||------ + \1 + tan (x)/*log(x)| - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|*|------ - ----------- + -------- + ------------------| + -------- + --------- + ---------- - --------------------------------------------------------------------- - ----------------------- + ---------------------- - ------------------------------------------- + ------------------------------------------------|
|| 2 x | |\ x / 2 3 \ x / | 2 x | x | 3 x \ x / | 2 3 2 4 x*log(x) x 2 | |\ x / 2 x | | 2 x 3 x*log(x) | 4 3 5 x*log(x) x 2 3 2 |
\\cos (x) / \ x x \ x / / x \cos (x) x x cos (x) x *log(x) / \ x / \ x cos (x) / x cos (x) cos (x) x x *log(x) x *log(x) /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
log(x)
$$- \frac{x^{\tan{\left(x \right)}} \left(3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(\frac{6 \sin^{2}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{2}{\cos^{2}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{2 \left(\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right)}{x \log{\left(x \right)}} + \frac{\left(1 + \frac{2}{\log{\left(x \right)}}\right) \left(\frac{1}{\cos^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{x}\right)}{x^{2} \log{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} - \frac{2 \tan{\left(x \right)}}{x^{3}}\right) + \left(\frac{1}{\cos^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{x}\right) \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} + 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} + \frac{2 \tan{\left(x \right)}}{x^{3}}\right) + 3 \left(\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{- \frac{1}{\cos^{2}{\left(x \right)}} + \frac{\tan{\left(x \right)}}{x}}{x \log{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right) \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) + \frac{24 \sin^{3}{\left(x \right)}}{\cos^{5}{\left(x \right)}} + \frac{16 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{x} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}}{x} - \frac{6 \left(\frac{3 \sin^{2}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{1}{\cos^{2}{\left(x \right)}} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} + \frac{\tan^{2}{\left(x \right)} + 1}{x^{2}} - \frac{\tan{\left(x \right)}}{x^{3}}\right)}{x \log{\left(x \right)}} + \frac{3 \left(1 + \frac{2}{\log{\left(x \right)}}\right) \left(\frac{2 \sin{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{\tan^{2}{\left(x \right)} + 1}{x} + \frac{\tan{\left(x \right)}}{x^{2}}\right)}{x^{2} \log{\left(x \right)}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{2}} - \frac{2 \left(\frac{1}{\cos^{2}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{x}\right) \left(1 + \frac{3}{\log{\left(x \right)}} + \frac{3}{\log{\left(x \right)}^{2}}\right)}{x^{3} \log{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{3}} + \frac{6 \tan{\left(x \right)}}{x^{4}}\right)}{\log{\left(x \right)}}$$
Gráfico