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^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Derivada de y=-6/x
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Expresiones idénticas
- y=arctg(4x)/(sinx+ dos)x= cero
- y es igual a arctg(4x) dividir por ( seno de x más 2)x es igual a 0
- y es igual a arctg(4x) dividir por ( seno de x más dos)x es igual a cero
- y=arctg4x/sinx+2x=0
- y=arctg(4x)/(sinx+2)x=O
- y=arctg(4x) dividir por (sinx+2)x=0
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Expresiones semejantes
- y=arctg(4x)/(sinx-2)x=0
Derivada de y=arctg(4x)/(sinx+2)x=0
Solución
Ha introducido
[src]
atan(4*x) ----------*x sin(x) + 2
$$x \frac{\operatorname{atan}{\left(4 x \right)}}{\sin{\left(x \right)} + 2}$$
(atan(4*x)/(sin(x) + 2))*x
Primera derivada
[src]
/ 4 atan(4*x)*cos(x)\ atan(4*x) x*|------------------------ - ----------------| + ---------- |/ 2\ 2 | sin(x) + 2 \\1 + 16*x /*(sin(x) + 2) (sin(x) + 2) /
$$x \left(- \frac{\cos{\left(x \right)} \operatorname{atan}{\left(4 x \right)}}{\left(\sin{\left(x \right)} + 2\right)^{2}} + \frac{4}{\left(16 x^{2} + 1\right) \left(\sin{\left(x \right)} + 2\right)}\right) + \frac{\operatorname{atan}{\left(4 x \right)}}{\sin{\left(x \right)} + 2}$$
Segunda derivada
[src]
/ / 2 \ \
| |2*cos (x) | |
| |---------- + sin(x)|*atan(4*x) |
8 | 128*x \2 + sin(x) / 8*cos(x) | 2*atan(4*x)*cos(x)
--------- - x*|------------ - ------------------------------- + ------------------------| - ------------------
2 | 2 2 + sin(x) / 2\ | 2 + sin(x)
1 + 16*x |/ 2\ \1 + 16*x /*(2 + sin(x))|
\\1 + 16*x / /
--------------------------------------------------------------------------------------------------------------
2 + sin(x)
$$\frac{- x \left(\frac{128 x}{\left(16 x^{2} + 1\right)^{2}} - \frac{\left(\sin{\left(x \right)} + \frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(x \right)} + 2}\right) \operatorname{atan}{\left(4 x \right)}}{\sin{\left(x \right)} + 2} + \frac{8 \cos{\left(x \right)}}{\left(16 x^{2} + 1\right) \left(\sin{\left(x \right)} + 2\right)}\right) - \frac{2 \cos{\left(x \right)} \operatorname{atan}{\left(4 x \right)}}{\sin{\left(x \right)} + 2} + \frac{8}{16 x^{2} + 1}}{\sin{\left(x \right)} + 2}$$
Tercera derivada
[src]
/ / 2 \ / 2 \ \
| | 64*x | / 2 \ | 6*sin(x) 6*cos (x) | | / 2 \
|128*|-1 + ---------| |2*cos (x) | |-1 + ---------- + -------------|*atan(4*x)*cos(x) | |2*cos (x) |
| | 2| 12*|---------- + sin(x)| | 2 + sin(x) 2| | 3*|---------- + sin(x)|*atan(4*x)
| \ 1 + 16*x / \2 + sin(x) / \ (2 + sin(x)) / 384*x*cos(x) | 384*x 24*cos(x) \2 + sin(x) /
x*|-------------------- + ------------------------ - -------------------------------------------------- + -------------------------| - ------------ - ------------------------ + ---------------------------------
| 2 / 2\ 2 + sin(x) 2 | 2 / 2\ 2 + sin(x)
| / 2\ \1 + 16*x /*(2 + sin(x)) / 2\ | / 2\ \1 + 16*x /*(2 + sin(x))
\ \1 + 16*x / \1 + 16*x / *(2 + sin(x))/ \1 + 16*x /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 + sin(x)
$$\frac{x \left(\frac{384 x \cos{\left(x \right)}}{\left(16 x^{2} + 1\right)^{2} \left(\sin{\left(x \right)} + 2\right)} - \frac{\left(-1 + \frac{6 \sin{\left(x \right)}}{\sin{\left(x \right)} + 2} + \frac{6 \cos^{2}{\left(x \right)}}{\left(\sin{\left(x \right)} + 2\right)^{2}}\right) \cos{\left(x \right)} \operatorname{atan}{\left(4 x \right)}}{\sin{\left(x \right)} + 2} + \frac{12 \left(\sin{\left(x \right)} + \frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(x \right)} + 2}\right)}{\left(16 x^{2} + 1\right) \left(\sin{\left(x \right)} + 2\right)} + \frac{128 \left(\frac{64 x^{2}}{16 x^{2} + 1} - 1\right)}{\left(16 x^{2} + 1\right)^{2}}\right) - \frac{384 x}{\left(16 x^{2} + 1\right)^{2}} + \frac{3 \left(\sin{\left(x \right)} + \frac{2 \cos^{2}{\left(x \right)}}{\sin{\left(x \right)} + 2}\right) \operatorname{atan}{\left(4 x \right)}}{\sin{\left(x \right)} + 2} - \frac{24 \cos{\left(x \right)}}{\left(16 x^{2} + 1\right) \left(\sin{\left(x \right)} + 2\right)}}{\sin{\left(x \right)} + 2}$$
Gráfico