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 7^(3*x-1)
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Derivada de 8*cos(x)^(3)
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Derivada de 4*x+8/x
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Derivada de 4^√x
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Expresiones idénticas
- (x*ln(2x+ uno)+arccos(5x))/((2x- uno)^ tres + uno)
- (x multiplicar por ln(2x más 1) más arc coseno de (5x)) dividir por ((2x menos 1) al cubo más 1)
- (x multiplicar por ln(2x más uno) más arc coseno de (5x)) dividir por ((2x menos uno) en el grado tres más uno)
- (x*ln(2x+1)+arccos(5x))/((2x-1)3+1)
- x*ln2x+1+arccos5x/2x-13+1
- (x*ln(2x+1)+arccos(5x))/((2x-1)³+1)
- (x*ln(2x+1)+arccos(5x))/((2x-1) en el grado 3+1)
- (xln(2x+1)+arccos(5x))/((2x-1)^3+1)
- (xln(2x+1)+arccos(5x))/((2x-1)3+1)
- xln2x+1+arccos5x/2x-13+1
- xln2x+1+arccos5x/2x-1^3+1
- (x*ln(2x+1)+arccos(5x)) dividir por ((2x-1)^3+1)
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Expresiones semejantes
- (x*ln(2x+1)-arccos(5x))/((2x-1)^3+1)
- (x*ln(2x+1)+arccos(5x))/((2x+1)^3+1)
- (x*ln(2x+1)+arccos(5x))/((2x-1)^3-1)
- (x*ln(2x-1)+arccos(5x))/((2x-1)^3+1)
Derivada de (x*ln(2x+1)+arccos(5x))/((2x-1)^3+1)
Solución
Ha introducido
[src]
x*log(2*x + 1) + acos(5*x)
--------------------------
3
(2*x - 1) + 1
$$\frac{x \log{\left(2 x + 1 \right)} + \operatorname{acos}{\left(5 x \right)}}{\left(2 x - 1\right)^{3} + 1}$$
(x*log(2*x + 1) + acos(5*x))/((2*x - 1)^3 + 1)
Primera derivada
[src]
5 2*x
- -------------- + ------- + log(2*x + 1)
___________ 2*x + 1
/ 2 2
\/ 1 - 25*x 6*(2*x - 1) *(x*log(2*x + 1) + acos(5*x))
----------------------------------------- - -----------------------------------------
3 2
(2*x - 1) + 1 / 3 \
\(2*x - 1) + 1/
$$- \frac{6 \left(2 x - 1\right)^{2} \left(x \log{\left(2 x + 1 \right)} + \operatorname{acos}{\left(5 x \right)}\right)}{\left(\left(2 x - 1\right)^{3} + 1\right)^{2}} + \frac{\frac{2 x}{2 x + 1} + \log{\left(2 x + 1 \right)} - \frac{5}{\sqrt{1 - 25 x^{2}}}}{\left(2 x - 1\right)^{3} + 1}$$
Segunda derivada
[src]
2 / 5 2*x \ / 3 \
12*(-1 + 2*x) *|- -------------- + ------- + log(1 + 2*x)| | 3*(-1 + 2*x) |
| ___________ 1 + 2*x | 24*(-1 + 2*x)*|-1 + ---------------|*(x*log(1 + 2*x) + acos(5*x))
| / 2 | | 3|
4 125*x 4*x \ \/ 1 - 25*x / \ 1 + (-1 + 2*x) /
------- - -------------- - ---------- - ---------------------------------------------------------- + -----------------------------------------------------------------
1 + 2*x 3/2 2 3 3
/ 2\ (1 + 2*x) 1 + (-1 + 2*x) 1 + (-1 + 2*x)
\1 - 25*x /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
1 + (-1 + 2*x)
$$\frac{- \frac{4 x}{\left(2 x + 1\right)^{2}} - \frac{125 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \frac{12 \left(2 x - 1\right)^{2} \left(\frac{2 x}{2 x + 1} + \log{\left(2 x + 1 \right)} - \frac{5}{\sqrt{1 - 25 x^{2}}}\right)}{\left(2 x - 1\right)^{3} + 1} + \frac{24 \left(2 x - 1\right) \left(x \log{\left(2 x + 1 \right)} + \operatorname{acos}{\left(5 x \right)}\right) \left(\frac{3 \left(2 x - 1\right)^{3}}{\left(2 x - 1\right)^{3} + 1} - 1\right)}{\left(2 x - 1\right)^{3} + 1} + \frac{4}{2 x + 1}}{\left(2 x - 1\right)^{3} + 1}$$
Tercera derivada
[src]
/ 3 6 \ / 3 \
| 18*(-1 + 2*x) 27*(-1 + 2*x) | 2 / 4 4*x 125*x \ | 3*(-1 + 2*x) | / 5 2*x \
48*(x*log(1 + 2*x) + acos(5*x))*|1 - --------------- + ------------------| 18*(-1 + 2*x) *|- ------- + ---------- + --------------| 72*(-1 + 2*x)*|-1 + ---------------|*|- -------------- + ------- + log(1 + 2*x)|
| 3 2| | 1 + 2*x 2 3/2| | 3| | ___________ 1 + 2*x |
2 | 1 + (-1 + 2*x) / 3\ | | (1 + 2*x) / 2\ | \ 1 + (-1 + 2*x) / | / 2 |
125 12 9375*x 16*x \ \1 + (-1 + 2*x) / / \ \1 - 25*x / / \ \/ 1 - 25*x /
- -------------- - ---------- - -------------- + ---------- - -------------------------------------------------------------------------- + -------------------------------------------------------- + --------------------------------------------------------------------------------
3/2 2 5/2 3 3 3 3
/ 2\ (1 + 2*x) / 2\ (1 + 2*x) 1 + (-1 + 2*x) 1 + (-1 + 2*x) 1 + (-1 + 2*x)
\1 - 25*x / \1 - 25*x /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3
1 + (-1 + 2*x)
$$\frac{- \frac{9375 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}}} + \frac{16 x}{\left(2 x + 1\right)^{3}} + \frac{18 \left(2 x - 1\right)^{2} \left(\frac{4 x}{\left(2 x + 1\right)^{2}} + \frac{125 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}} - \frac{4}{2 x + 1}\right)}{\left(2 x - 1\right)^{3} + 1} + \frac{72 \left(2 x - 1\right) \left(\frac{3 \left(2 x - 1\right)^{3}}{\left(2 x - 1\right)^{3} + 1} - 1\right) \left(\frac{2 x}{2 x + 1} + \log{\left(2 x + 1 \right)} - \frac{5}{\sqrt{1 - 25 x^{2}}}\right)}{\left(2 x - 1\right)^{3} + 1} - \frac{48 \left(x \log{\left(2 x + 1 \right)} + \operatorname{acos}{\left(5 x \right)}\right) \left(\frac{27 \left(2 x - 1\right)^{6}}{\left(\left(2 x - 1\right)^{3} + 1\right)^{2}} - \frac{18 \left(2 x - 1\right)^{3}}{\left(2 x - 1\right)^{3} + 1} + 1\right)}{\left(2 x - 1\right)^{3} + 1} - \frac{12}{\left(2 x + 1\right)^{2}} - \frac{125}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}}}}{\left(2 x - 1\right)^{3} + 1}$$
Gráfico