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 x^-0,2
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Derivada de e-x
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Derivada de e^e
- Derivada de e^((3*x)^2)
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Expresiones idénticas
- y=arctg(3x*e^√tgx)
- y es igual a arctg(3x multiplicar por e en el grado √tgx)
- y=arctg(3x*e√tgx)
- y=arctg3x*e√tgx
- y=arctg(3xe^√tgx)
- y=arctg(3xe√tgx)
- y=arctg3xe√tgx
- y=arctg3xe^√tgx
Derivada de y=arctg(3x*e^√tgx)
Solución
Ha introducido
[src]
/ ________\
| \/ tan(x) |
atan\3*x*E /
$$\operatorname{atan}{\left(e^{\sqrt{\tan{\left(x \right)}}} 3 x \right)}$$
atan((3*x)*E^(sqrt(tan(x))))
Primera derivada
[src]
/ 2 \ ________
|1 tan (x)| \/ tan(x)
________ 3*x*|- + -------|*e
\/ tan(x) \2 2 /
3*e + -----------------------------
________
\/ tan(x)
---------------------------------------------
________
2 2*\/ tan(x)
1 + 9*x *e
$$\frac{\frac{3 x \left(\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}\right) e^{\sqrt{\tan{\left(x \right)}}}}{\sqrt{\tan{\left(x \right)}}} + 3 e^{\sqrt{\tan{\left(x \right)}}}}{9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1}$$
Segunda derivada
[src]
/ 2 \
| / / 2 \\ ________|
| | x*\1 + tan (x)/| 2*\/ tan(x) |
| 18*x*|2 + ---------------| *e |
| / / 2 \ / 2 \\ | ________ | | ________
|/ 2 \ | 4 ________ x*\1 + tan (x)/ x*\1 + tan (x)/| \ \/ tan(x) / | \/ tan(x)
3*|\1 + tan (x)/*|---------- + 4*x*\/ tan(x) + --------------- - ---------------| - -----------------------------------------|*e
| | ________ tan(x) 3/2 | ________ |
| \\/ tan(x) tan (x) / 2 2*\/ tan(x) |
\ 1 + 9*x *e /
-------------------------------------------------------------------------------------------------------------------------------------------
/ ________\
| 2 2*\/ tan(x) |
4*\1 + 9*x *e /
$$\frac{3 \left(- \frac{18 x \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 2\right)^{2} e^{2 \sqrt{\tan{\left(x \right)}}}}{9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{\frac{3}{2}}{\left(x \right)}} + 4 x \sqrt{\tan{\left(x \right)}} + \frac{4}{\sqrt{\tan{\left(x \right)}}}\right)\right) e^{\sqrt{\tan{\left(x \right)}}}}{4 \left(9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1\right)}$$
Tercera derivada
[src]
/ / 2 2 2\ 3 / 2 2 \ \
| | / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ / 2 \ | / / 2 \\ ________ / / 2 \\ | 2 / 2 \ 2 / 2 \ / 2 \| ________ / / 2 \\ / / 2 \ / 2 \\ ________|
|/ 2 \ | ________ 6*\1 + tan (x)/ 6*\1 + tan (x)/ / 2 \ 3/2 x*\1 + tan (x)/ 4*x*\1 + tan (x)/ 3*x*\1 + tan (x)/ 3*x*\1 + tan (x)/ | 2 | x*\1 + tan (x)/| 4*\/ tan(x) | x*\1 + tan (x)/| | x *\1 + tan (x)/ 2*x *\1 + tan (x)/ 2 ________ / 2 \ 8*x*\1 + tan (x)/| 2*\/ tan(x) / 2 \ | x*\1 + tan (x)/| | 4 ________ x*\1 + tan (x)/ x*\1 + tan (x)/| 2*\/ tan(x) |
|\1 + tan (x)/*|24*\/ tan(x) - --------------- + --------------- + 12*x*\1 + tan (x)/ + 16*x*tan (x) + ---------------- - ----------------- - ------------------ + ------------------| 81*x *|2 + ---------------| *e 9*|2 + ---------------|*|4 - ----------------- + ------------------- + 4*x *\/ tan(x) *\1 + tan (x)/ + -----------------|*e 9*x*\1 + tan (x)/*|2 + ---------------|*|---------- + 4*x*\/ tan(x) + --------------- - ---------------|*e |
| | 3/2 tan(x) 3/2 ________ 2 5/2 | | ________ | | ________ | | 3/2 tan(x) ________ | | ________ | | ________ tan(x) 3/2 | | ________
| \ tan (x) tan (x) \/ tan(x) tan (x) tan (x) / \ \/ tan(x) / \ \/ tan(x) / \ tan (x) \/ tan(x) / \ \/ tan(x) / \\/ tan(x) tan (x) / | \/ tan(x)
3*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------|*e
| 8 2 / ________\ / ________\ |
| / ________\ | 2 2*\/ tan(x) | | 2 2*\/ tan(x) | |
| | 2 2*\/ tan(x) | 4*\1 + 9*x *e / 2*\1 + 9*x *e / |
\ \1 + 9*x *e / /
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
________
2 2*\/ tan(x)
1 + 9*x *e
$$\frac{3 \left(\frac{81 x^{2} \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 2\right)^{3} e^{4 \sqrt{\tan{\left(x \right)}}}}{\left(9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1\right)^{2}} - \frac{9 x \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{\frac{3}{2}}{\left(x \right)}} + 4 x \sqrt{\tan{\left(x \right)}} + \frac{4}{\sqrt{\tan{\left(x \right)}}}\right) e^{2 \sqrt{\tan{\left(x \right)}}}}{2 \left(9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1\right)} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{3 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{3}{2}}{\left(x \right)}} + \frac{3 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{5}{2}}{\left(x \right)}} + 12 x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{4 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 16 x \tan^{\frac{3}{2}}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{\frac{3}{2}}{\left(x \right)}} + 24 \sqrt{\tan{\left(x \right)}}\right)}{8} - \frac{9 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 2\right) \left(\frac{2 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} - \frac{x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{3}{2}}{\left(x \right)}} + 4 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\tan{\left(x \right)}} + \frac{8 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 4\right) e^{2 \sqrt{\tan{\left(x \right)}}}}{4 \left(9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1\right)}\right) e^{\sqrt{\tan{\left(x \right)}}}}{9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1}$$
Gráfico