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
-
¿Cómo usar?
- Derivada de:
-
Derivada de 2*cos(3*x)
-
Derivada de x^(7/6)
-
Derivada de x^(2/5)
-
Derivada de 1/ln(x)
-
Expresiones idénticas
- x^(sqrt(dos +sin(tres *x)^(dos)))
- x en el grado ( raíz cuadrada de (2 más seno de (3 multiplicar por x) en el grado (2)))
- x en el grado ( raíz cuadrada de (dos más seno de (tres multiplicar por x) en el grado (dos)))
- x^(√(2+sin(3*x)^(2)))
- x(sqrt(2+sin(3*x)(2)))
- xsqrt2+sin3*x2
- x^(sqrt(2+sin(3x)^(2)))
- x(sqrt(2+sin(3x)(2)))
- xsqrt2+sin3x2
- x^sqrt2+sin3x^2
-
Expresiones semejantes
- x^(sqrt(2-sin(3*x)^(2)))
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt(x)^3+1
- sqrt(x)*i^n*(sqrt(x)+sqrt(x+1))
- sqrt5x
- sqrt(x)-cos(x)+2
- sqrt(x)*asin(sqrt(x))+sqrt(1-x)
- Seno sin
- sin(t)*cos(t)
- sin(3*x^2)/((3*x^2))
- sin(3*x-pi/12)
- sin(5*x+2)
- sin(2*y)
Derivada de x^(sqrt(2+sin(3*x)^(2)))
Solución
Ha introducido
[src]
_______________ / 2 \/ 2 + sin (3*x) x
$$x^{\sqrt{\sin^{2}{\left(3 x \right)} + 2}}$$
x^(sqrt(2 + sin(3*x)^2))
Solución detallada
-
No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
-
Simplificamos:
Respuesta:
Primera derivada
[src]
_______________ / _______________ \
/ 2 | / 2 |
\/ 2 + sin (3*x) |\/ 2 + sin (3*x) 3*cos(3*x)*log(x)*sin(3*x)|
x *|------------------ + --------------------------|
| x _______________ |
| / 2 |
\ \/ 2 + sin (3*x) /
$$x^{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} \left(\frac{3 \log{\left(x \right)} \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} + \frac{\sqrt{\sin^{2}{\left(3 x \right)} + 2}}{x}\right)$$
Segunda derivada
[src]
/ 2 \
_______________ |/ _______________ \ _______________ |
/ 2 || / 2 | / 2 2 2 2 2 |
\/ 2 + sin (3*x) ||\/ 2 + sin (3*x) 3*cos(3*x)*log(x)*sin(3*x)| \/ 2 + sin (3*x) 9*sin (3*x)*log(x) 9*cos (3*x)*log(x) 9*cos (3*x)*sin (3*x)*log(x) 6*cos(3*x)*sin(3*x) |
x *||------------------ + --------------------------| - ------------------ - ------------------ + ------------------ - ---------------------------- + --------------------|
|| x _______________ | 2 _______________ _______________ 3/2 _______________|
|| / 2 | x / 2 / 2 / 2 \ / 2 |
\\ \/ 2 + sin (3*x) / \/ 2 + sin (3*x) \/ 2 + sin (3*x) \2 + sin (3*x)/ x*\/ 2 + sin (3*x) /
$$x^{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} \left(\left(\frac{3 \log{\left(x \right)} \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} + \frac{\sqrt{\sin^{2}{\left(3 x \right)} + 2}}{x}\right)^{2} - \frac{9 \log{\left(x \right)} \sin^{2}{\left(3 x \right)}}{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} + \frac{9 \log{\left(x \right)} \cos^{2}{\left(3 x \right)}}{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} - \frac{9 \log{\left(x \right)} \sin^{2}{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{\left(\sin^{2}{\left(3 x \right)} + 2\right)^{\frac{3}{2}}} + \frac{6 \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{x \sqrt{\sin^{2}{\left(3 x \right)} + 2}} - \frac{\sqrt{\sin^{2}{\left(3 x \right)} + 2}}{x^{2}}\right)$$
Tercera derivada
[src]
/ 3 \
_______________ |/ _______________ \ / _______________ \ / _______________ \ _______________ |
/ 2 || / 2 | | / 2 | | / 2 2 2 2 2 | / 2 2 2 3 2 2 3 3 3 |
\/ 2 + sin (3*x) ||\/ 2 + sin (3*x) 3*cos(3*x)*log(x)*sin(3*x)| |\/ 2 + sin (3*x) 3*cos(3*x)*log(x)*sin(3*x)| |\/ 2 + sin (3*x) 9*cos (3*x)*log(x) 9*sin (3*x)*log(x) 6*cos(3*x)*sin(3*x) 9*cos (3*x)*sin (3*x)*log(x)| 2*\/ 2 + sin (3*x) 27*sin (3*x) 27*cos (3*x) 108*cos(3*x)*log(x)*sin(3*x) 81*cos (3*x)*log(x)*sin(3*x) 27*cos (3*x)*sin (3*x) 9*cos(3*x)*sin(3*x) 81*cos (3*x)*sin (3*x)*log(x) 81*sin (3*x)*cos(3*x)*log(x)|
x *||------------------ + --------------------------| - 3*|------------------ + --------------------------|*|------------------ - ------------------ + ------------------ - -------------------- + ----------------------------| + -------------------- - -------------------- + -------------------- - ---------------------------- - ---------------------------- - ---------------------- - --------------------- + ----------------------------- + ----------------------------|
|| x _______________ | | x _______________ | | 2 _______________ _______________ _______________ 3/2 | 3 _______________ _______________ _______________ 3/2 3/2 _______________ 5/2 3/2 |
|| / 2 | | / 2 | | x / 2 / 2 / 2 / 2 \ | x / 2 / 2 / 2 / 2 \ / 2 \ 2 / 2 / 2 \ / 2 \ |
\\ \/ 2 + sin (3*x) / \ \/ 2 + sin (3*x) / \ \/ 2 + sin (3*x) \/ 2 + sin (3*x) x*\/ 2 + sin (3*x) \2 + sin (3*x)/ / x*\/ 2 + sin (3*x) x*\/ 2 + sin (3*x) \/ 2 + sin (3*x) \2 + sin (3*x)/ x*\2 + sin (3*x)/ x *\/ 2 + sin (3*x) \2 + sin (3*x)/ \2 + sin (3*x)/ /
$$x^{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} \left(\left(\frac{3 \log{\left(x \right)} \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} + \frac{\sqrt{\sin^{2}{\left(3 x \right)} + 2}}{x}\right)^{3} - 3 \left(\frac{3 \log{\left(x \right)} \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} + \frac{\sqrt{\sin^{2}{\left(3 x \right)} + 2}}{x}\right) \left(\frac{9 \log{\left(x \right)} \sin^{2}{\left(3 x \right)}}{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} - \frac{9 \log{\left(x \right)} \cos^{2}{\left(3 x \right)}}{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} + \frac{9 \log{\left(x \right)} \sin^{2}{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{\left(\sin^{2}{\left(3 x \right)} + 2\right)^{\frac{3}{2}}} - \frac{6 \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{x \sqrt{\sin^{2}{\left(3 x \right)} + 2}} + \frac{\sqrt{\sin^{2}{\left(3 x \right)} + 2}}{x^{2}}\right) - \frac{108 \log{\left(x \right)} \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{\sqrt{\sin^{2}{\left(3 x \right)} + 2}} + \frac{81 \log{\left(x \right)} \sin^{3}{\left(3 x \right)} \cos{\left(3 x \right)}}{\left(\sin^{2}{\left(3 x \right)} + 2\right)^{\frac{3}{2}}} - \frac{81 \log{\left(x \right)} \sin{\left(3 x \right)} \cos^{3}{\left(3 x \right)}}{\left(\sin^{2}{\left(3 x \right)} + 2\right)^{\frac{3}{2}}} + \frac{81 \log{\left(x \right)} \sin^{3}{\left(3 x \right)} \cos^{3}{\left(3 x \right)}}{\left(\sin^{2}{\left(3 x \right)} + 2\right)^{\frac{5}{2}}} - \frac{27 \sin^{2}{\left(3 x \right)}}{x \sqrt{\sin^{2}{\left(3 x \right)} + 2}} + \frac{27 \cos^{2}{\left(3 x \right)}}{x \sqrt{\sin^{2}{\left(3 x \right)} + 2}} - \frac{27 \sin^{2}{\left(3 x \right)} \cos^{2}{\left(3 x \right)}}{x \left(\sin^{2}{\left(3 x \right)} + 2\right)^{\frac{3}{2}}} - \frac{9 \sin{\left(3 x \right)} \cos{\left(3 x \right)}}{x^{2} \sqrt{\sin^{2}{\left(3 x \right)} + 2}} + \frac{2 \sqrt{\sin^{2}{\left(3 x \right)} + 2}}{x^{3}}\right)$$
Gráfico