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=th^ dos (x+ tres)/arctansqrtx
- y es igual a th al cuadrado (x más 3) dividir por arc tangente de raíz cuadrada de x
- y es igual a th en el grado dos (x más tres) dividir por arc tangente de raíz cuadrada de x
- y=th^2(x+3)/arctan√x
- y=th2(x+3)/arctansqrtx
- y=th2x+3/arctansqrtx
- y=th²(x+3)/arctansqrtx
- y=th en el grado 2(x+3)/arctansqrtx
- y=th^2x+3/arctansqrtx
- y=th^2(x+3) dividir por arctansqrtx
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Expresiones semejantes
- y=th^2(x-3)/arctansqrtx
Derivada de y=th^2(x+3)/arctansqrtx
Solución
Ha introducido
[src]
2
tanh (x + 3)
------------
/ ___\
atan\\/ x /
$$\frac{\tanh^{2}{\left(x + 3 \right)}}{\operatorname{atan}{\left(\sqrt{x} \right)}}$$
tanh(x + 3)^2/atan(sqrt(x))
Primera derivada
[src]
/ 2 \ 2
\2 - 2*tanh (x + 3)/*tanh(x + 3) tanh (x + 3)
-------------------------------- - ----------------------------
/ ___\ ___ 2/ ___\
atan\\/ x / 2*\/ x *(1 + x)*atan \\/ x /
$$\frac{\left(2 - 2 \tanh^{2}{\left(x + 3 \right)}\right) \tanh{\left(x + 3 \right)}}{\operatorname{atan}{\left(\sqrt{x} \right)}} - \frac{\tanh^{2}{\left(x + 3 \right)}}{2 \sqrt{x} \left(x + 1\right) \operatorname{atan}^{2}{\left(\sqrt{x} \right)}}$$
Segunda derivada
[src]
2 / 1 2 2 \
tanh (3 + x)*|---- + ------------- + ---------------------|
| 3/2 ___ / ___\| / 2 \
/ 2 \ / 2 \ \x \/ x *(1 + x) x*(1 + x)*atan\\/ x // 2*\-1 + tanh (3 + x)/*tanh(3 + x)
2*\-1 + tanh (3 + x)/*\-1 + 3*tanh (3 + x)/ + ----------------------------------------------------------- + ---------------------------------
/ ___\ ___ / ___\
4*(1 + x)*atan\\/ x / \/ x *(1 + x)*atan\\/ x /
---------------------------------------------------------------------------------------------------------------------------------------------
/ ___\
atan\\/ x /
$$\frac{2 \left(\tanh^{2}{\left(x + 3 \right)} - 1\right) \left(3 \tanh^{2}{\left(x + 3 \right)} - 1\right) + \frac{\left(\frac{2}{x \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{2}{\sqrt{x} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right) \tanh^{2}{\left(x + 3 \right)}}{4 \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{2 \left(\tanh^{2}{\left(x + 3 \right)} - 1\right) \tanh{\left(x + 3 \right)}}{\sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}}{\operatorname{atan}{\left(\sqrt{x} \right)}}$$
Tercera derivada
[src]
/ 2 / 3 4 8 6 6 12 \ / 2 \ / 1 2 2 \ \
| tanh (3 + x)*|---- + ------------ + -------------- + ---------------------- + -------------------------- + ----------------------| 3*\-1 + tanh (3 + x)/*|---- + ------------- + ---------------------|*tanh(3 + x)|
| | 5/2 3/2 ___ 2 2 / ___\ 3/2 2 2/ ___\ 2 / ___\| / 2 \ / 2 \ | 3/2 ___ / ___\| |
| / 2 \ / 2 \ \x x *(1 + x) \/ x *(1 + x) x *(1 + x)*atan\\/ x / x *(1 + x) *atan \\/ x / x*(1 + x) *atan\\/ x // 3*\-1 + tanh (3 + x)/*\-1 + 3*tanh (3 + x)/ \x \/ x *(1 + x) x*(1 + x)*atan\\/ x // |
-|8*\-1 + tanh (3 + x)/*\-2 + 3*tanh (3 + x)/*tanh(3 + x) + ---------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------- + --------------------------------------------------------------------------------|
| / ___\ ___ / ___\ / ___\ |
\ 8*(1 + x)*atan\\/ x / \/ x *(1 + x)*atan\\/ x / 2*(1 + x)*atan\\/ x / /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ___\
atan\\/ x /
$$- \frac{8 \left(\tanh^{2}{\left(x + 3 \right)} - 1\right) \left(3 \tanh^{2}{\left(x + 3 \right)} - 2\right) \tanh{\left(x + 3 \right)} + \frac{3 \left(\tanh^{2}{\left(x + 3 \right)} - 1\right) \left(\frac{2}{x \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{2}{\sqrt{x} \left(x + 1\right)} + \frac{1}{x^{\frac{3}{2}}}\right) \tanh{\left(x + 3 \right)}}{2 \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{\left(\frac{12}{x \left(x + 1\right)^{2} \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{6}{x^{2} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{8}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{4}{x^{\frac{3}{2}} \left(x + 1\right)} + \frac{6}{x^{\frac{3}{2}} \left(x + 1\right)^{2} \operatorname{atan}^{2}{\left(\sqrt{x} \right)}} + \frac{3}{x^{\frac{5}{2}}}\right) \tanh^{2}{\left(x + 3 \right)}}{8 \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}} + \frac{3 \left(\tanh^{2}{\left(x + 3 \right)} - 1\right) \left(3 \tanh^{2}{\left(x + 3 \right)} - 1\right)}{\sqrt{x} \left(x + 1\right) \operatorname{atan}{\left(\sqrt{x} \right)}}}{\operatorname{atan}{\left(\sqrt{x} \right)}}$$
Gráfico