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- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
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- Derivada de:
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Derivada de 2
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Derivada de 1/(1+x^2)
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Derivada de sin(x/2)
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Derivada de x^2*sin(x)
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Expresiones idénticas
- y=ln^5x*arctan7x^ cuatro
- y es igual a ln en el grado 5x multiplicar por arc tangente de 7x en el grado 4
- y es igual a ln en el grado 5x multiplicar por arc tangente de 7x en el grado cuatro
- y=ln5x*arctan7x4
- y=ln⁵x*arctan7x⁴
- y=ln^5xarctan7x^4
- y=ln5xarctan7x4
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Expresiones con funciones
- ln
- lnx
- ln(sin(x))
- ln(1+x^2)
- ln(3x)
- ln(x+sqrt(x^2+1))
Derivada de y=ln^5x*arctan7x^4
Solución
Ha introducido
[src]
5 4 log (x)*atan (7*x)
$$\log{\left(x \right)}^{5} \operatorname{atan}^{4}{\left(7 x \right)}$$
log(x)^5*atan(7*x)^4
Primera derivada
[src]
4 4 3 5
5*atan (7*x)*log (x) 28*atan (7*x)*log (x)
-------------------- + ---------------------
x 2
1 + 49*x
$$\frac{28 \log{\left(x \right)}^{5} \operatorname{atan}^{3}{\left(7 x \right)}}{49 x^{2} + 1} + \frac{5 \log{\left(x \right)}^{4} \operatorname{atan}^{4}{\left(7 x \right)}}{x}$$
Segunda derivada
[src]
/ 2 2 \
2 3 | 196*log (x)*(-3 + 14*x*atan(7*x)) 5*atan (7*x)*(-4 + log(x)) 280*atan(7*x)*log(x)|
atan (7*x)*log (x)*|- --------------------------------- - -------------------------- + --------------------|
| 2 2 / 2\ |
| / 2\ x x*\1 + 49*x / |
\ \1 + 49*x / /
$$\left(- \frac{196 \left(14 x \operatorname{atan}{\left(7 x \right)} - 3\right) \log{\left(x \right)}^{2}}{\left(49 x^{2} + 1\right)^{2}} + \frac{280 \log{\left(x \right)} \operatorname{atan}{\left(7 x \right)}}{x \left(49 x^{2} + 1\right)} - \frac{5 \left(\log{\left(x \right)} - 4\right) \operatorname{atan}^{2}{\left(7 x \right)}}{x^{2}}\right) \log{\left(x \right)}^{3} \operatorname{atan}^{2}{\left(7 x \right)}$$
Tercera derivada
[src]
/ / 2 2 \ \
| 3 | 2 3 63*x*atan(7*x) 196*x *atan (7*x)| |
| 1372*log (x)*|- atan (7*x) + --------- - -------------- + -----------------| |
| 3 / 2 \ | 2 2 2 | 2 2 |
2 |5*atan (7*x)*\6 + log (x) - 6*log(x)/ \ 1 + 49*x 1 + 49*x 1 + 49*x / 1470*log (x)*(-3 + 14*x*atan(7*x))*atan(7*x) 210*atan (7*x)*(-4 + log(x))*log(x)|
2*log (x)*|------------------------------------- + ---------------------------------------------------------------------------- - -------------------------------------------- - -----------------------------------|*atan(7*x)
| 3 2 2 2 / 2\ |
| x / 2\ / 2\ x *\1 + 49*x / |
\ \1 + 49*x / x*\1 + 49*x / /
$$2 \left(\frac{1372 \left(\frac{196 x^{2} \operatorname{atan}^{2}{\left(7 x \right)}}{49 x^{2} + 1} - \frac{63 x \operatorname{atan}{\left(7 x \right)}}{49 x^{2} + 1} - \operatorname{atan}^{2}{\left(7 x \right)} + \frac{3}{49 x^{2} + 1}\right) \log{\left(x \right)}^{3}}{\left(49 x^{2} + 1\right)^{2}} - \frac{1470 \left(14 x \operatorname{atan}{\left(7 x \right)} - 3\right) \log{\left(x \right)}^{2} \operatorname{atan}{\left(7 x \right)}}{x \left(49 x^{2} + 1\right)^{2}} - \frac{210 \left(\log{\left(x \right)} - 4\right) \log{\left(x \right)} \operatorname{atan}^{2}{\left(7 x \right)}}{x^{2} \left(49 x^{2} + 1\right)} + \frac{5 \left(\log{\left(x \right)}^{2} - 6 \log{\left(x \right)} + 6\right) \operatorname{atan}^{3}{\left(7 x \right)}}{x^{3}}\right) \log{\left(x \right)}^{2} \operatorname{atan}{\left(7 x \right)}$$
Gráfico