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:
-
Derivada de x^(3*x)
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Derivada de -2x
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Derivada de x^3*sin(x)
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Derivada de (sqrt(x)-1)/sqrt(x^2-x-1)
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Expresiones idénticas
- y=ln(arcsin5x)+arccos(lnx)
- y es igual a ln(arc seno de 5x) más arc coseno de (lnx)
- y=lnarcsin5x+arccoslnx
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Expresiones semejantes
- y=ln(arcsin5x)-arccos(lnx)
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Expresiones con funciones
- ln
- ln(x)^2
- ln(1+2x)
- ln((x+1)/(x-1))
- ln((1+x)/(1-x))
- ln(1+e^x)
- arccos
- arccos((x-1)/(2-x))
- arccos4
- arccos^2(x)
- arccos(1/x)
- arccos(2^x)
- lnx
- lnx/x^2
- lnx-sinx
- lnx/e^x^2
- lnx/x^3
- lnx+4x^5
Derivada de y=ln(arcsin5x)+arccos(lnx)
Solución
Ha introducido
[src]
log(asin(5*x)) + acos(log(x))
$$\log{\left(\operatorname{asin}{\left(5 x \right)} \right)} + \operatorname{acos}{\left(\log{\left(x \right)} \right)}$$
log(asin(5*x)) + acos(log(x))
Primera derivada
[src]
1 5
- ------------------ + ------------------------
_____________ ___________
/ 2 / 2
x*\/ 1 - log (x) \/ 1 - 25*x *asin(5*x)
$$\frac{5}{\sqrt{1 - 25 x^{2}} \operatorname{asin}{\left(5 x \right)}} - \frac{1}{x \sqrt{1 - \log{\left(x \right)}^{2}}}$$
Segunda derivada
[src]
1 25 log(x) 125*x
------------------- + ----------------------- - ------------------- + ------------------------
_____________ / 2\ 2 3/2 3/2
2 / 2 \-1 + 25*x /*asin (5*x) 2 / 2 \ / 2\
x *\/ 1 - log (x) x *\1 - log (x)/ \1 - 25*x / *asin(5*x)
$$\frac{125 x}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{25}{\left(25 x^{2} - 1\right) \operatorname{asin}^{2}{\left(5 x \right)}} + \frac{1}{x^{2} \sqrt{1 - \log{\left(x \right)}^{2}}} - \frac{\log{\left(x \right)}}{x^{2} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{3}{2}}}$$
5-я производная
[src]
3 4 2 2 3 2 2 4
35 24 9 28125 62500 75000 41015625*x 105*log (x) 105*log (x) 90*log (x) 50*log(x) 90*log(x) 150*log (x) 859375*x 937500*x 7031250*x 7031250*x 205078125*x
- ------------------- - ------------------- - ------------------- + ------------------------ + ------------------------- + ------------------------- - ------------------------ - ------------------- - ------------------- - ------------------- + ------------------- + ------------------- + ------------------- + ------------------------ + ------------------------ + ------------------------ + ------------------------- + ------------------------
3/2 _____________ 5/2 5/2 5/2 5/2 4 9/2 5/2 7/2 3/2 5/2 7/2 3 3 7/2 7/2 9/2
5 / 2 \ 5 / 2 5 / 2 \ / 2\ / 2\ 3 / 2\ 5 / 2\ 2 5 / 2 \ 5 / 2 \ 5 / 2 \ 5 / 2 \ 5 / 2 \ 5 / 2 \ / 2\ 2 / 2\ 4 / 2\ / 2\ 3 / 2\
x *\1 - log (x)/ x *\/ 1 - log (x) x *\1 - log (x)/ \1 - 25*x / *asin(5*x) \1 - 25*x / *asin (5*x) \1 - 25*x / *asin (5*x) \-1 + 25*x / *asin (5*x) x *\1 - log (x)/ x *\1 - log (x)/ x *\1 - log (x)/ x *\1 - log (x)/ x *\1 - log (x)/ x *\1 - log (x)/ \-1 + 25*x / *asin (5*x) \-1 + 25*x / *asin (5*x) \1 - 25*x / *asin(5*x) \1 - 25*x / *asin (5*x) \1 - 25*x / *asin(5*x)
$$\frac{205078125 x^{4}}{\left(1 - 25 x^{2}\right)^{\frac{9}{2}} \operatorname{asin}{\left(5 x \right)}} - \frac{41015625 x^{3}}{\left(25 x^{2} - 1\right)^{4} \operatorname{asin}^{2}{\left(5 x \right)}} + \frac{7031250 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{7}{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{7031250 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{7}{2}} \operatorname{asin}^{3}{\left(5 x \right)}} + \frac{859375 x}{\left(25 x^{2} - 1\right)^{3} \operatorname{asin}^{2}{\left(5 x \right)}} + \frac{937500 x}{\left(25 x^{2} - 1\right)^{3} \operatorname{asin}^{4}{\left(5 x \right)}} + \frac{28125}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{62500}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}} \operatorname{asin}^{3}{\left(5 x \right)}} + \frac{75000}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}} \operatorname{asin}^{5}{\left(5 x \right)}} - \frac{24}{x^{5} \sqrt{1 - \log{\left(x \right)}^{2}}} + \frac{50 \log{\left(x \right)}}{x^{5} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{3}{2}}} - \frac{35}{x^{5} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{3}{2}}} - \frac{105 \log{\left(x \right)}^{2}}{x^{5} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{5}{2}}} + \frac{90 \log{\left(x \right)}}{x^{5} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{5}{2}}} - \frac{9}{x^{5} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{5}{2}}} + \frac{150 \log{\left(x \right)}^{3}}{x^{5} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{7}{2}}} - \frac{90 \log{\left(x \right)}^{2}}{x^{5} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{7}{2}}} - \frac{105 \log{\left(x \right)}^{4}}{x^{5} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{9}{2}}}$$
Tercera derivada
[src]
2 2
1 2 125 250 1875*x 3*log (x) 3*log(x) 9375*x
- ------------------- - ------------------- + ------------------------ + ------------------------- - ------------------------ - ------------------- + ------------------- + ------------------------
3/2 _____________ 3/2 3/2 2 5/2 3/2 5/2
3 / 2 \ 3 / 2 / 2\ / 2\ 3 / 2\ 2 3 / 2 \ 3 / 2 \ / 2\
x *\1 - log (x)/ x *\/ 1 - log (x) \1 - 25*x / *asin(5*x) \1 - 25*x / *asin (5*x) \-1 + 25*x / *asin (5*x) x *\1 - log (x)/ x *\1 - log (x)/ \1 - 25*x / *asin(5*x)
$$\frac{9375 x^{2}}{\left(1 - 25 x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(5 x \right)}} - \frac{1875 x}{\left(25 x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(5 x \right)}} + \frac{125}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(5 x \right)}} + \frac{250}{\left(1 - 25 x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(5 x \right)}} - \frac{2}{x^{3} \sqrt{1 - \log{\left(x \right)}^{2}}} + \frac{3 \log{\left(x \right)}}{x^{3} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{3}{2}}} - \frac{1}{x^{3} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{3}{2}}} - \frac{3 \log{\left(x \right)}^{2}}{x^{3} \left(1 - \log{\left(x \right)}^{2}\right)^{\frac{5}{2}}}$$
Gráfico