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 (-4)/x^2
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Derivada de 2/x²
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Derivada de -2*y
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Derivada de (3+2x)/(x-5)
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Expresiones idénticas
- y=(sin(tres *x))^arccos*x
- y es igual a ( seno de (3 multiplicar por x)) en el grado arc coseno de multiplicar por x
- y es igual a ( seno de (tres multiplicar por x)) en el grado arc coseno de multiplicar por x
- y=(sin(3*x))arccos*x
- y=sin3*xarccos*x
- y=(sin(3x))^arccosx
- y=(sin(3x))arccosx
- y=sin3xarccosx
- y=sin3x^arccosx
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Expresiones con funciones
- Seno sin
- sin(x)^4
- sin(x/3+3)+2*x
- sin(x)^sin(x)
- sin(x)/(1-x)
- sin(x^2+3)
Derivada de y=(sin(3*x))^arccos*x
Solución
Ha introducido
[src]
acos(x) sin (3*x)
$$\sin^{\operatorname{acos}{\left(x \right)}}{\left(3 x \right)}$$
sin(3*x)^acos(x)
Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
Primera derivada
[src]
acos(x) / log(sin(3*x)) 3*acos(x)*cos(3*x)\
sin (3*x)*|- ------------- + ------------------|
| ________ sin(3*x) |
| / 2 |
\ \/ 1 - x /
$$\left(\frac{3 \cos{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin{\left(3 x \right)}} - \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \sin^{\operatorname{acos}{\left(x \right)}}{\left(3 x \right)}$$
Segunda derivada
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/ 2 2 \
acos(x) |/ log(sin(3*x)) 3*acos(x)*cos(3*x)\ x*log(sin(3*x)) 9*cos (3*x)*acos(x) 6*cos(3*x) |
sin (3*x)*||- ------------- + ------------------| - 9*acos(x) - --------------- - ------------------- - --------------------|
|| ________ sin(3*x) | 3/2 2 ________ |
|| / 2 | / 2\ sin (3*x) / 2 |
\\ \/ 1 - x / \1 - x / \/ 1 - x *sin(3*x)/
$$\left(- \frac{x \log{\left(\sin{\left(3 x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(\frac{3 \cos{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin{\left(3 x \right)}} - \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{\sqrt{1 - x^{2}}}\right)^{2} - 9 \operatorname{acos}{\left(x \right)} - \frac{9 \cos^{2}{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin^{2}{\left(3 x \right)}} - \frac{6 \cos{\left(3 x \right)}}{\sqrt{1 - x^{2}} \sin{\left(3 x \right)}}\right) \sin^{\operatorname{acos}{\left(x \right)}}{\left(3 x \right)}$$
Tercera derivada
[src]
/ 3 / 2 \ 2 2 3 \
acos(x) |/ log(sin(3*x)) 3*acos(x)*cos(3*x)\ 27 log(sin(3*x)) / log(sin(3*x)) 3*acos(x)*cos(3*x)\ | x*log(sin(3*x)) 6*cos(3*x) 9*cos (3*x)*acos(x)| 3*x *log(sin(3*x)) 27*cos (3*x) 54*cos (3*x)*acos(x) 54*acos(x)*cos(3*x) 9*x*cos(3*x) |
sin (3*x)*||- ------------- + ------------------| + ----------- - ------------- - 3*|- ------------- + ------------------|*|9*acos(x) + --------------- + -------------------- + -------------------| - ------------------ + --------------------- + -------------------- + ------------------- - --------------------|
|| ________ sin(3*x) | ________ 3/2 | ________ sin(3*x) | | 3/2 ________ 2 | 5/2 ________ 3 sin(3*x) 3/2 |
|| / 2 | / 2 / 2\ | / 2 | | / 2\ / 2 sin (3*x) | / 2\ / 2 2 sin (3*x) / 2\ |
\\ \/ 1 - x / \/ 1 - x \1 - x / \ \/ 1 - x / \ \1 - x / \/ 1 - x *sin(3*x) / \1 - x / \/ 1 - x *sin (3*x) \1 - x / *sin(3*x)/
$$\left(- \frac{3 x^{2} \log{\left(\sin{\left(3 x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{9 x \cos{\left(3 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \sin{\left(3 x \right)}} + \left(\frac{3 \cos{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin{\left(3 x \right)}} - \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{\sqrt{1 - x^{2}}}\right)^{3} - 3 \left(\frac{3 \cos{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin{\left(3 x \right)}} - \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \left(\frac{x \log{\left(\sin{\left(3 x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 9 \operatorname{acos}{\left(x \right)} + \frac{9 \cos^{2}{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin^{2}{\left(3 x \right)}} + \frac{6 \cos{\left(3 x \right)}}{\sqrt{1 - x^{2}} \sin{\left(3 x \right)}}\right) + \frac{54 \cos{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin{\left(3 x \right)}} + \frac{54 \cos^{3}{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin^{3}{\left(3 x \right)}} + \frac{27}{\sqrt{1 - x^{2}}} + \frac{27 \cos^{2}{\left(3 x \right)}}{\sqrt{1 - x^{2}} \sin^{2}{\left(3 x \right)}} - \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \sin^{\operatorname{acos}{\left(x \right)}}{\left(3 x \right)}$$
3-я производная
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/ 3 / 2 \ 2 2 3 \
acos(x) |/ log(sin(3*x)) 3*acos(x)*cos(3*x)\ 27 log(sin(3*x)) / log(sin(3*x)) 3*acos(x)*cos(3*x)\ | x*log(sin(3*x)) 6*cos(3*x) 9*cos (3*x)*acos(x)| 3*x *log(sin(3*x)) 27*cos (3*x) 54*cos (3*x)*acos(x) 54*acos(x)*cos(3*x) 9*x*cos(3*x) |
sin (3*x)*||- ------------- + ------------------| + ----------- - ------------- - 3*|- ------------- + ------------------|*|9*acos(x) + --------------- + -------------------- + -------------------| - ------------------ + --------------------- + -------------------- + ------------------- - --------------------|
|| ________ sin(3*x) | ________ 3/2 | ________ sin(3*x) | | 3/2 ________ 2 | 5/2 ________ 3 sin(3*x) 3/2 |
|| / 2 | / 2 / 2\ | / 2 | | / 2\ / 2 sin (3*x) | / 2\ / 2 2 sin (3*x) / 2\ |
\\ \/ 1 - x / \/ 1 - x \1 - x / \ \/ 1 - x / \ \1 - x / \/ 1 - x *sin(3*x) / \1 - x / \/ 1 - x *sin (3*x) \1 - x / *sin(3*x)/
$$\left(- \frac{3 x^{2} \log{\left(\sin{\left(3 x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{9 x \cos{\left(3 x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \sin{\left(3 x \right)}} + \left(\frac{3 \cos{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin{\left(3 x \right)}} - \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{\sqrt{1 - x^{2}}}\right)^{3} - 3 \left(\frac{3 \cos{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin{\left(3 x \right)}} - \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{\sqrt{1 - x^{2}}}\right) \left(\frac{x \log{\left(\sin{\left(3 x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + 9 \operatorname{acos}{\left(x \right)} + \frac{9 \cos^{2}{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin^{2}{\left(3 x \right)}} + \frac{6 \cos{\left(3 x \right)}}{\sqrt{1 - x^{2}} \sin{\left(3 x \right)}}\right) + \frac{54 \cos{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin{\left(3 x \right)}} + \frac{54 \cos^{3}{\left(3 x \right)} \operatorname{acos}{\left(x \right)}}{\sin^{3}{\left(3 x \right)}} + \frac{27}{\sqrt{1 - x^{2}}} + \frac{27 \cos^{2}{\left(3 x \right)}}{\sqrt{1 - x^{2}} \sin^{2}{\left(3 x \right)}} - \frac{\log{\left(\sin{\left(3 x \right)} \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \sin^{\operatorname{acos}{\left(x \right)}}{\left(3 x \right)}$$
Gráfico