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!
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Derivada de e^x*x^3
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Derivada de e^x/x^2
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Expresiones idénticas
- y=ln(sin4x^ dos)× cinco ^ctg2x/tg7x
- y es igual a ln( seno de 4x al cuadrado )×5 en el grado ctg2x dividir por tg7x
- y es igual a ln( seno de 4x en el grado dos)× cinco en el grado ctg2x dividir por tg7x
- y=ln(sin4x2)×5ctg2x/tg7x
- y=lnsin4x2×5ctg2x/tg7x
- y=ln(sin4x²)×5^ctg2x/tg7x
- y=ln(sin4x en el grado 2)×5 en el grado ctg2x/tg7x
- y=lnsin4x^2×5^ctg2x/tg7x
- y=ln(sin4x^2)×5^ctg2x dividir por tg7x
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Expresiones con funciones
- ln
- ln(2x)/x
- ln|x|
- ln^2(2x-1)
- ln(x+√(x²+1))
- ln*(x+sqrt*(x^2+1))
Derivada de y=ln(sin4x^2)×5^ctg2x/tg7x
Solución
Ha introducido
[src]
/ 2 \ cot(2*x)
log\sin (4*x)/*5
------------------------
tan(7*x)
$$\frac{5^{\cot{\left(2 x \right)}} \log{\left(\sin^{2}{\left(4 x \right)} \right)}}{\tan{\left(7 x \right)}}$$
(log(sin(4*x)^2)*5^cot(2*x))/tan(7*x)
Primera derivada
[src]
cot(2*x)
8*5 *cos(4*x) cot(2*x) / 2 \ / 2 \
-------------------- + 5 *\-2 - 2*cot (2*x)/*log(5)*log\sin (4*x)/ cot(2*x) / 2 \ / 2 \
sin(4*x) 5 *\-7 - 7*tan (7*x)/*log\sin (4*x)/
------------------------------------------------------------------------- + -------------------------------------------
tan(7*x) 2
tan (7*x)
$$\frac{5^{\cot{\left(2 x \right)}} \left(- 7 \tan^{2}{\left(7 x \right)} - 7\right) \log{\left(\sin^{2}{\left(4 x \right)} \right)}}{\tan^{2}{\left(7 x \right)}} + \frac{5^{\cot{\left(2 x \right)}} \left(- 2 \cot^{2}{\left(2 x \right)} - 2\right) \log{\left(5 \right)} \log{\left(\sin^{2}{\left(4 x \right)} \right)} + \frac{8 \cdot 5^{\cot{\left(2 x \right)}} \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}}}{\tan{\left(7 x \right)}}$$
Segunda derivada
[src]
/ / 2 \ / 4*cos(4*x) / 2 \ / 2 \\ \
| 2 14*\1 + tan (7*x)/*|- ---------- + \1 + cot (2*x)/*log(5)*log\sin (4*x)/| / 2 \ / 2 \ |
cot(2*x) | 16*cos (4*x) \ sin(4*x) / / 2 \ | 1 + tan (7*x)| / 2 \ 16*\1 + cot (2*x)/*cos(4*x)*log(5) / 2 \ / / 2 \ \ / 2 \|
2*5 *|-16 - ------------ + ------------------------------------------------------------------------- + 49*\1 + tan (7*x)/*|-1 + -------------|*log\sin (4*x)/ - ---------------------------------- + 2*\1 + cot (2*x)/*\2*cot(2*x) + \1 + cot (2*x)/*log(5)/*log(5)*log\sin (4*x)/|
| 2 tan(7*x) | 2 | sin(4*x) |
\ sin (4*x) \ tan (7*x) / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
tan(7*x)
$$\frac{2 \cdot 5^{\cot{\left(2 x \right)}} \left(49 \left(\frac{\tan^{2}{\left(7 x \right)} + 1}{\tan^{2}{\left(7 x \right)}} - 1\right) \left(\tan^{2}{\left(7 x \right)} + 1\right) \log{\left(\sin^{2}{\left(4 x \right)} \right)} + 2 \left(\left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} + 2 \cot{\left(2 x \right)}\right) \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} \log{\left(\sin^{2}{\left(4 x \right)} \right)} + \frac{14 \left(\left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} \log{\left(\sin^{2}{\left(4 x \right)} \right)} - \frac{4 \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}}\right) \left(\tan^{2}{\left(7 x \right)} + 1\right)}{\tan{\left(7 x \right)}} - \frac{16 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}} - 16 - \frac{16 \cos^{2}{\left(4 x \right)}}{\sin^{2}{\left(4 x \right)}}\right)}{\tan{\left(7 x \right)}}$$
Tercera derivada
[src]
/ / / 2 \ \ \
| | | cos (4*x)| | |
| | 32*|1 + ---------|*cos(4*x) | |
| | / 2 \ | 2 | / 2 \ / 2 \ / / 2 \ \ | / 2 / 2 \ \ / 2 \ |
| | / 2 \ | cos (4*x)| \ sin (4*x)/ / 2 \ | 2 / 2 \ 2 / 2 \ | / 2 \ 12*\1 + cot (2*x)/*\2*cot(2*x) + \1 + cot (2*x)/*log(5)/*cos(4*x)*log(5)| / 2 \ | 8*cos (4*x) / 2 \ / / 2 \ \ / 2 \ 8*\1 + cot (2*x)/*cos(4*x)*log(5)| / 2 \ | 1 + tan (7*x)| / 4*cos(4*x) / 2 \ / 2 \\|
| / 2 3\ 4*|24*\1 + cot (2*x)/*|1 + ---------|*log(5) + --------------------------- - \1 + cot (2*x)/*\2 + 6*cot (2*x) + \1 + cot (2*x)/ *log (5) + 6*\1 + cot (2*x)/*cot(2*x)*log(5)/*log(5)*log\sin (4*x)/ + ------------------------------------------------------------------------| 42*\1 + tan (7*x)/*|8 + ----------- - \1 + cot (2*x)/*\2*cot(2*x) + \1 + cot (2*x)/*log(5)/*log(5)*log\sin (4*x)/ + ---------------------------------| 294*\1 + tan (7*x)/*|-1 + -------------|*|- ---------- + \1 + cot (2*x)/*log(5)*log\sin (4*x)/||
| | / 2 \ / 2 \ | | | 2 | sin(4*x) sin(4*x) | | 2 sin(4*x) | | 2 | \ sin(4*x) /|
cot(2*x) | | 2 5*\1 + tan (7*x)/ 3*\1 + tan (7*x)/ | / 2 \ \ \ sin (4*x)/ / \ sin (4*x) / \ tan (7*x) / |
2*5 *|- 343*|2 + 2*tan (7*x) - ------------------ + ------------------|*log\sin (4*x)/ + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------------|
| | 2 4 | tan(7*x) 2 tan(7*x) |
\ \ tan (7*x) tan (7*x) / tan (7*x) /
$$2 \cdot 5^{\cot{\left(2 x \right)}} \left(- \frac{294 \left(\frac{\tan^{2}{\left(7 x \right)} + 1}{\tan^{2}{\left(7 x \right)}} - 1\right) \left(\left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} \log{\left(\sin^{2}{\left(4 x \right)} \right)} - \frac{4 \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}}\right) \left(\tan^{2}{\left(7 x \right)} + 1\right)}{\tan{\left(7 x \right)}} + \frac{42 \left(\tan^{2}{\left(7 x \right)} + 1\right) \left(- \left(\left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} + 2 \cot{\left(2 x \right)}\right) \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} \log{\left(\sin^{2}{\left(4 x \right)} \right)} + \frac{8 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}} + 8 + \frac{8 \cos^{2}{\left(4 x \right)}}{\sin^{2}{\left(4 x \right)}}\right)}{\tan^{2}{\left(7 x \right)}} - 343 \left(\frac{3 \left(\tan^{2}{\left(7 x \right)} + 1\right)^{3}}{\tan^{4}{\left(7 x \right)}} - \frac{5 \left(\tan^{2}{\left(7 x \right)} + 1\right)^{2}}{\tan^{2}{\left(7 x \right)}} + 2 \tan^{2}{\left(7 x \right)} + 2\right) \log{\left(\sin^{2}{\left(4 x \right)} \right)} + \frac{4 \left(24 \left(1 + \frac{\cos^{2}{\left(4 x \right)}}{\sin^{2}{\left(4 x \right)}}\right) \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} + \frac{32 \left(1 + \frac{\cos^{2}{\left(4 x \right)}}{\sin^{2}{\left(4 x \right)}}\right) \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}} + \frac{12 \left(\left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} + 2 \cot{\left(2 x \right)}\right) \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} \cos{\left(4 x \right)}}{\sin{\left(4 x \right)}} - \left(\cot^{2}{\left(2 x \right)} + 1\right) \left(\left(\cot^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(5 \right)}^{2} + 6 \left(\cot^{2}{\left(2 x \right)} + 1\right) \log{\left(5 \right)} \cot{\left(2 x \right)} + 6 \cot^{2}{\left(2 x \right)} + 2\right) \log{\left(5 \right)} \log{\left(\sin^{2}{\left(4 x \right)} \right)}\right)}{\tan{\left(7 x \right)}}\right)$$
Gráfico