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 1/(x+3)
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Derivada de 4*y
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Derivada de (-1)/x-3*x
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Derivada de y=csc(3x²+1)
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Expresiones idénticas
- y= tres ^sin^ siete (x^ dos + dos /√x)
- y es igual a 3 en el grado seno de en el grado 7(x al cuadrado más 2 dividir por √x)
- y es igual a tres en el grado seno de en el grado siete (x en el grado dos más dos dividir por √x)
- y=3sin7(x2+2/√x)
- y=3sin7x2+2/√x
- y=3^sin⁷(x²+2/√x)
- y=3 en el grado sin en el grado 7(x en el grado 2+2/√x)
- y=3^sin^7x^2+2/√x
- y=3^sin^7(x^2+2 dividir por √x)
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Expresiones semejantes
- y=3^sin^7(x^2-2/√x)
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Expresiones con funciones
- Seno sin
- sin(x+π)
- sin(x)^(2)*2^x^2
- sin^n(x)
- sin(x)^(32)*cos(8*x)^5
- sin(7*x)^(2)
Derivada de y=3^sin^7(x^2+2/√x)
Solución
Ha introducido
[src]
7/ 2 2 \
sin |x + -----|
| ___|
\ \/ x /
3
$$3^{\sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}}$$
3^(sin(x^2 + 2/sqrt(x))^7)
Primera derivada
[src]
7/ 2 2 \
sin |x + -----|
| ___|
\ \/ x / 6/ 2 2 \ / 1 \ / 2 2 \
7*3 *sin |x + -----|*|- ---- + 2*x|*cos|x + -----|*log(3)
| ___| | 3/2 | | ___|
\ \/ x / \ x / \ \/ x /
$$7 \cdot 3^{\sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}} \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right) \log{\left(3 \right)} \sin^{6}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}$$
Segunda derivada
[src]
7/ 2 2 \ / / 3 \ / 2 2 \ / 2 2 \ \
sin |x + -----| | |4 + ----|*cos|x + -----|*sin|x + -----| |
| ___| | 2 2 | 5/2| | ___| | ___| 2 |
\ \/ x / 5/ 2 2 \ | / 1 \ 2/ 2 2 \ / 1 \ 2/ 2 2 \ \ x / \ \/ x / \ \/ x / / 1 \ 2/ 2 2 \ 7/ 2 2 \ |
7*3 *sin |x + -----|*|- |- ---- + 2*x| *sin |x + -----| + 6*|- ---- + 2*x| *cos |x + -----| + ------------------------------------------ + 7*|- ---- + 2*x| *cos |x + -----|*sin |x + -----|*log(3)|*log(3)
| ___| | | 3/2 | | ___| | 3/2 | | ___| 2 | 3/2 | | ___| | ___| |
\ \/ x / \ \ x / \ \/ x / \ x / \ \/ x / \ x / \ \/ x / \ \/ x / /
$$7 \cdot 3^{\sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}} \left(\frac{\left(4 + \frac{3}{x^{\frac{5}{2}}}\right) \sin{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}}{2} + 7 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{2} \log{\left(3 \right)} \sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} - \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{2} \sin^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} + 6 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{2} \cos^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}\right) \log{\left(3 \right)} \sin^{5}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}$$
Tercera derivada
[src]
7/ 2 2 \ / 2/ 2 2 \ / 2 2 \ 3/ 2 2 \ / 3 \ / 1 \ 2/ 2 2 \ 8/ 2 2 \ / 3 \ / 1 \ \
sin |x + -----| | 15*sin |x + -----|*cos|x + -----| 3*sin |x + -----|*|4 + ----|*|- ---- + 2*x| 21*cos |x + -----|*sin |x + -----|*|4 + ----|*|- ---- + 2*x|*log(3)|
| ___| | 3 3 | ___| | ___| | ___| | 5/2| | 3/2 | 3 3 3 | ___| | ___| | 5/2| | 3/2 | |
\ \/ x / 4/ 2 2 \ | / 1 \ 3/ 2 2 \ / 1 \ 2/ 2 2 \ / 2 2 \ \ \/ x / \ \/ x / \ \/ x / \ x / \ x / / 1 \ 9/ 2 2 \ / 2 2 \ 2/ 2 2 \ / 3 \ / 1 \ / 2 2 \ / 1 \ 3/ 2 2 \ 2 14/ 2 2 \ / 1 \ 3/ 2 2 \ 7/ 2 2 \ \ \/ x / \ \/ x / \ x / \ x / |
7*3 *sin |x + -----|*|30*|- ---- + 2*x| *cos |x + -----| - 19*|- ---- + 2*x| *sin |x + -----|*cos|x + -----| - ----------------------------------- - -------------------------------------------- - 21*|- ---- + 2*x| *sin |x + -----|*cos|x + -----|*log(3) + 9*cos |x + -----|*|4 + ----|*|- ---- + 2*x|*sin|x + -----| + 49*|- ---- + 2*x| *cos |x + -----|*log (3)*sin |x + -----| + 126*|- ---- + 2*x| *cos |x + -----|*sin |x + -----|*log(3) + ---------------------------------------------------------------------|*log(3)
| ___| | | 3/2 | | ___| | 3/2 | | ___| | ___| 7/2 2 | 3/2 | | ___| | ___| | ___| | 5/2| | 3/2 | | ___| | 3/2 | | ___| | ___| | 3/2 | | ___| | ___| 2 |
\ \/ x / \ \ x / \ \/ x / \ x / \ \/ x / \ \/ x / 4*x \ x / \ \/ x / \ \/ x / \ \/ x / \ x / \ x / \ \/ x / \ x / \ \/ x / \ \/ x / \ x / \ \/ x / \ \/ x / /
$$7 \cdot 3^{\sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}} \left(\frac{21 \left(4 + \frac{3}{x^{\frac{5}{2}}}\right) \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right) \log{\left(3 \right)} \sin^{8}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}}{2} - \frac{3 \left(4 + \frac{3}{x^{\frac{5}{2}}}\right) \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right) \sin^{3}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}}{2} + 9 \left(4 + \frac{3}{x^{\frac{5}{2}}}\right) \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right) \sin{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} + 49 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{3} \log{\left(3 \right)}^{2} \sin^{14}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos^{3}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} - 21 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{3} \log{\left(3 \right)} \sin^{9}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} + 126 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{3} \log{\left(3 \right)} \sin^{7}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos^{3}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} - 19 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{3} \sin^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} + 30 \left(2 x - \frac{1}{x^{\frac{3}{2}}}\right)^{3} \cos^{3}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} - \frac{15 \sin^{2}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)} \cos{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}}{4 x^{\frac{7}{2}}}\right) \log{\left(3 \right)} \sin^{4}{\left(x^{2} + \frac{2}{\sqrt{x}} \right)}$$