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- 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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- Derivada de:
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Derivada de y=8t³+3t²+2
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Derivada de y=(׳+1)^10
- Derivada de y=cx^2
- Derivada de y=2*3,14*n*t
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Expresiones idénticas
- (x*sqrt(ln(x)*(ctg(x))^ tres)/((x^ cinco + nueve)^ ocho *(dos - tres x)^(uno / tres)))^ uno /3
- (x multiplicar por raíz cuadrada de (ln(x) multiplicar por (ctg(x)) al cubo ) dividir por ((x en el grado 5 más 9) en el grado 8 multiplicar por (2 menos 3x) en el grado (1 dividir por 3))) en el grado 1 dividir por 3
- (x multiplicar por raíz cuadrada de (ln(x) multiplicar por (ctg(x)) en el grado tres) dividir por ((x en el grado cinco más nueve) en el grado ocho multiplicar por (dos menos tres x) en el grado (uno dividir por tres))) en el grado uno dividir por 3
- (x*√(ln(x)*(ctg(x))^3)/((x^5+9)^8*(2-3x)^(1/3)))^1/3
- (x*sqrt(ln(x)*(ctg(x))3)/((x5+9)8*(2-3x)(1/3)))1/3
- x*sqrtlnx*ctgx3/x5+98*2-3x1/31/3
- (x*sqrt(ln(x)*(ctg(x))³)/((x⁵+9)⁸*(2-3x)^(1/3)))^1/3
- (x*sqrt(ln(x)*(ctg(x)) en el grado 3)/((x en el grado 5+9) en el grado 8*(2-3x) en el grado (1/3))) en el grado 1/3
- (xsqrt(ln(x)(ctg(x))^3)/((x^5+9)^8(2-3x)^(1/3)))^1/3
- (xsqrt(ln(x)(ctg(x))3)/((x5+9)8(2-3x)(1/3)))1/3
- xsqrtlnxctgx3/x5+982-3x1/31/3
- xsqrtlnxctgx^3/x^5+9^82-3x^1/3^1/3
- (x*sqrt(ln(x)*(ctg(x))^3) dividir por ((x^5+9)^8*(2-3x)^(1 dividir por 3)))^1 dividir por 3
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Expresiones semejantes
- (x*sqrt(ln(x)*(ctg(x))^3)/((x^5-9)^8*(2-3x)^(1/3)))^1/3
- (x*sqrt(ln(x)*(ctg(x))^3)/((x^5+9)^8*(2+3x)^(1/3)))^1/3
Derivada de (x*sqrt(ln(x)*(ctg(x))^3)/((x^5+9)^8*(2-3x)^(1/3)))^1/3
Solución
Ha introducido
[src]
_______________________
/ ________________
/ / 3
/ x*\/ log(x)*cot (x)
/ ---------------------
/ 8
3 / / 5 \ 3 _________
\/ \x + 9/ *\/ 2 - 3*x
$$\sqrt[3]{\frac{x \sqrt{\log{\left(x \right)} \cot^{3}{\left(x \right)}}}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)^{8}}}$$
((x*sqrt(log(x)*cot(x)^3))/(((x^5 + 9)^8*(2 - 3*x)^(1/3))))^(1/3)
Primera derivada
[src]
/ / ________________ / 3 2 / 2 \ \\ \
| | / 3 |cot (x) cot (x)*\-3 - 3*cot (x)/*log(x)|| |
| | ________________ x*\/ cot (x)*log(x) *|------- + -------------------------------|| / 8 \|
| 1 | / 3 \ 2*x 2 /| ________________ | / 5 \ 7||
|---------------------*|\/ log(x)*cot (x) + -----------------------------------------------------------------| / 3 | \x + 9/ 4 3 _________ / 5 \ ||
_____________________________________________ | 8 | 3 | x*\/ cot (x)*log(x) *|------------ - 40*x *\/ 2 - 3*x *\x + 9/ ||
/ ________________ 8 |3 _________ / 5 \ \ cot (x)*log(x) / | 2/3 ||
/ / 3 1 3 _________ / 5 \ |\/ 2 - 3*x *\x + 9/ \(2 - 3*x) /|
/ x*\/ cot (x)*log(x) *--------------------- *\/ 2 - 3*x *\x + 9/ *|--------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------|
/ 8 | 3 16 |
3 / 3 _________ / 5 \ | 2/3 / 5 \ |
\/ \/ 2 - 3*x *\x + 9/ \ 3*(2 - 3*x) *\x + 9/ /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
________________
/ 3
x*\/ cot (x)*log(x)
$$\frac{\sqrt[3]{x \frac{1}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)^{8}} \sqrt{\log{\left(x \right)} \cot^{3}{\left(x \right)}}} \sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)^{8} \left(\frac{x \sqrt{\log{\left(x \right)} \cot^{3}{\left(x \right)}} \left(- 40 x^{4} \sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)^{7} + \frac{\left(x^{5} + 9\right)^{8}}{\left(2 - 3 x\right)^{\frac{2}{3}}}\right)}{3 \left(2 - 3 x\right)^{\frac{2}{3}} \left(x^{5} + 9\right)^{16}} + \frac{\frac{1}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)^{8}} \left(\frac{x \sqrt{\log{\left(x \right)} \cot^{3}{\left(x \right)}} \left(\frac{\left(- 3 \cot^{2}{\left(x \right)} - 3\right) \log{\left(x \right)} \cot^{2}{\left(x \right)}}{2} + \frac{\cot^{3}{\left(x \right)}}{2 x}\right)}{\log{\left(x \right)} \cot^{3}{\left(x \right)}} + \sqrt{\log{\left(x \right)} \cot^{3}{\left(x \right)}}\right)}{3}\right)}{x \sqrt{\log{\left(x \right)} \cot^{3}{\left(x \right)}}}$$
Segunda derivada
[src]
/ / / 2 2 / 2 \ \ \ \
| | |cot (x) / 2 \ 2 / 2 \ 6*\1 + cot (x)/*cot(x)| 2 / 2 \ | |
| | / cot(x) / 2 \ \ 2*x*|------- - 6*\1 + cot (x)/ *log(x) - 6*cot (x)*\1 + cot (x)/*log(x) + ----------------------| / cot(x) / 2 \ \ / 2 \ / cot(x) / 2 \ \ / 5 \ / 5 \ / 5 \ | / 5\ 4 / 5\ | / 5 \| |
| / / 5 \\ | 2*|- ------ + 3*\1 + cot (x)/*log(x)| | 2 x | x*|- ------ + 3*\1 + cot (x)/*log(x)| 6*x*\1 + cot (x)/*|- ------ + 3*\1 + cot (x)/*log(x)| | 9 + x 4 3 _________| 5 | 9 + x 4 3 _________| | 9 + x 4 3 _________| | \9 + x / 8 3 _________ 40*x *\9 + x / 3 3 _________ / 5\| / cot(x) / 2 \ \ | 9 + x 4 3 _________|| / / 5 \\ / / 5 \\ / / 5 \\ / / 5 \\|
| | | 9 + x 4 3 _________|| | / / cot(x) / 2 \ \\ 4*cot(x) \ x / / 2 \ \ x / \ x / \ x / 4*|- ------------ + 40*x *\/ 2 - 3*x | 320*x *|- ------------ + 40*x *\/ 2 - 3*x | 8*x*|- ------------ + 40*x *\/ 2 - 3*x | 8*x*|- ------------ + 700*x *\/ 2 - 3*x - -------------- + 80*x *\/ 2 - 3*x *\9 + x /| 2*x*|- ------ + 3*\1 + cot (x)/*log(x)|*|- ------------ + 40*x *\/ 2 - 3*x || | | 9 + x 4 3 _________|| | | 9 + x 4 3 _________|| | | 9 + x 4 3 _________|| | | 9 + x 4 3 _________|||
| | / cot(x) / 2 \ \ 2*x*|- ------------ + 40*x *\/ 2 - 3*x || | | x*|- ------ + 3*\1 + cot (x)/*log(x)|| / 4 \ - -------- - ------------------------------------- + 12*\1 + cot (x)/*log(x) + ------------------------------------------------------------------------------------------------- - -------------------------------------- + ----------------------------------------------------- | 2/3 | | 2/3 | | 2/3 | | 5/3 2/3 | \ x / | 2/3 || / / cot(x) / 2 \ \\ | / cot(x) / 2 \ \ 2*x*|- ------------ + 40*x *\/ 2 - 3*x || | / cot(x) / 2 \ \ 2*x*|- ------------ + 40*x *\/ 2 - 3*x || | / cot(x) / 2 \ \ 2*x*|- ------------ + 40*x *\/ 2 - 3*x || | / cot(x) / 2 \ \ 2*x*|- ------------ + 40*x *\/ 2 - 3*x |||
| | x*|- ------ + 3*\1 + cot (x)/*log(x)| | 2/3 || | | \ x /| | 1 40*x | x log(x) cot(x) cot(x)*log(x) cot(x) \ (2 - 3*x) / \ (2 - 3*x) / \ (2 - 3*x) / \ (2 - 3*x) (2 - 3*x) / \ (2 - 3*x) /| | / 4 \ x*|- ------ + 3*\1 + cot (x)/*log(x)|| | x*|- ------ + 3*\1 + cot (x)/*log(x)| | 2/3 || | x*|- ------ + 3*\1 + cot (x)/*log(x)| | 2/3 || | x*|- ------ + 3*\1 + cot (x)/*log(x)| | 2/3 || | x*|- ------ + 3*\1 + cot (x)/*log(x)| | 2/3 |||
_______________________ | | \ x / \ (2 - 3*x) /| 3*|- 2*|-2 + -------------------------------------|*|- ------- + ------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------- - ------------------------------------------- + ---------------------------------------- + --------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------| | | 1 40*x | \ x /| | \ x / \ (2 - 3*x) /| 3 | \ x / \ (2 - 3*x) /| | \ x / \ (2 - 3*x) /| / cot(x) / 2 \ \ | \ x / \ (2 - 3*x) /||
/ ________________ |3*|-2 + ------------------------------------- + ----------------------------------------| | \ cot(x)*log(x) / | 2 - 3*x 5| cot(x)*log(x) 3 _________ / 5\ 2 4/3 / 5\ 2 3 _________ / 5\ | |-2 + 2*x*|- ------- + ------| + -------------------------------------|*|-2 + ------------------------------------- + ----------------------------------------| 120*x *|-2 + ------------------------------------- + ----------------------------------------| 3*|-2 + ------------------------------------- + ----------------------------------------| 3*|- ------ + 3*\1 + cot (x)/*log(x)|*|-2 + ------------------------------------- + ----------------------------------------||
/ / 3 | | cot(x)*log(x) 3 _________ / 5\ | | \ 9 + x / \/ 2 - 3*x *\9 + x / 3 _________ / 5\ (2 - 3*x) *\9 + x / 3 _________ / 5\ \/ 2 - 3*x *\9 + x /*cot(x)*log(x) | | | 2 - 3*x 5| cot(x)*log(x) | | cot(x)*log(x) 3 _________ / 5\ | | cot(x)*log(x) 3 _________ / 5\ | | cot(x)*log(x) 3 _________ / 5\ | \ x / | cot(x)*log(x) 3 _________ / 5\ ||
/ x*\/ cot (x)*log(x) | \ \/ 2 - 3*x *\9 + x / / \ \/ 2 - 3*x *\9 + x / \/ 2 - 3*x *\9 + x / / \ \ 9 + x / / \ \/ 2 - 3*x *\9 + x / / \ \/ 2 - 3*x *\9 + x / / \ \/ 2 - 3*x *\9 + x / / \ \/ 2 - 3*x *\9 + x / /|
/ --------------------- *|----------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------|
/ 8 | 2 2*x 2 5 x*(2 - 3*x) 2*x*cot(x)*log(x) |
3 / 3 _________ / 5\ \ x 2*x 9 + x /
\/ \/ 2 - 3*x *\9 + x /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
18
$$\frac{\sqrt[3]{\frac{x \sqrt{\log{\left(x \right)} \cot^{3}{\left(x \right)}}}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)^{8}}} \left(- \frac{120 x^{3} \left(\frac{x \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right)}{\log{\left(x \right)} \cot{\left(x \right)}} + \frac{2 x \left(40 x^{4} \sqrt[3]{2 - 3 x} - \frac{x^{5} + 9}{\left(2 - 3 x\right)^{\frac{2}{3}}}\right)}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)} - 2\right)}{x^{5} + 9} - \frac{3 \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right) \left(\frac{x \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right)}{\log{\left(x \right)} \cot{\left(x \right)}} + \frac{2 x \left(40 x^{4} \sqrt[3]{2 - 3 x} - \frac{x^{5} + 9}{\left(2 - 3 x\right)^{\frac{2}{3}}}\right)}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)} - 2\right)}{2 x \log{\left(x \right)} \cot{\left(x \right)}} - \frac{3 \left(- \frac{320 x^{5} \left(40 x^{4} \sqrt[3]{2 - 3 x} - \frac{x^{5} + 9}{\left(2 - 3 x\right)^{\frac{2}{3}}}\right)}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)^{2}} - \frac{2 x \left(40 x^{4} \sqrt[3]{2 - 3 x} - \frac{x^{5} + 9}{\left(2 - 3 x\right)^{\frac{2}{3}}}\right) \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right)}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right) \log{\left(x \right)} \cot{\left(x \right)}} + \frac{8 x \left(700 x^{8} \sqrt[3]{2 - 3 x} - \frac{40 x^{4} \left(x^{5} + 9\right)}{\left(2 - 3 x\right)^{\frac{2}{3}}} + 80 x^{3} \sqrt[3]{2 - 3 x} \left(x^{5} + 9\right) - \frac{\left(x^{5} + 9\right)^{2}}{\left(2 - 3 x\right)^{\frac{5}{3}}}\right)}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)^{2}} + \frac{8 x \left(40 x^{4} \sqrt[3]{2 - 3 x} - \frac{x^{5} + 9}{\left(2 - 3 x\right)^{\frac{2}{3}}}\right)}{\left(2 - 3 x\right)^{\frac{4}{3}} \left(x^{5} + 9\right)} - 2 \left(\frac{40 x^{4}}{x^{5} + 9} - \frac{1}{2 - 3 x}\right) \left(\frac{x \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right)}{\log{\left(x \right)} \cot{\left(x \right)}} - 2\right) + \frac{- \frac{x \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right)^{2}}{\log{\left(x \right)} \cot{\left(x \right)}} + \frac{6 x \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} + \frac{2 x \left(- 6 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} - 6 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \cot^{2}{\left(x \right)} + \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{x} + \frac{\cot^{2}{\left(x \right)}}{x^{2}}\right)}{\cot{\left(x \right)}} - \frac{2 \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right)}{\log{\left(x \right)}} + 12 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{4 \cot{\left(x \right)}}{x}}{\log{\left(x \right)} \cot{\left(x \right)}} + \frac{4 \left(40 x^{4} \sqrt[3]{2 - 3 x} - \frac{x^{5} + 9}{\left(2 - 3 x\right)^{\frac{2}{3}}}\right)}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)}\right)}{2 x} + \frac{3 \left(\frac{x \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right)}{\log{\left(x \right)} \cot{\left(x \right)}} + \frac{2 x \left(40 x^{4} \sqrt[3]{2 - 3 x} - \frac{x^{5} + 9}{\left(2 - 3 x\right)^{\frac{2}{3}}}\right)}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)} - 2\right)}{x \left(2 - 3 x\right)} + \frac{\left(2 x \left(\frac{40 x^{4}}{x^{5} + 9} - \frac{1}{2 - 3 x}\right) + \frac{x \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right)}{\log{\left(x \right)} \cot{\left(x \right)}} - 2\right) \left(\frac{x \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right)}{\log{\left(x \right)} \cot{\left(x \right)}} + \frac{2 x \left(40 x^{4} \sqrt[3]{2 - 3 x} - \frac{x^{5} + 9}{\left(2 - 3 x\right)^{\frac{2}{3}}}\right)}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)} - 2\right)}{2 x^{2}} + \frac{3 \left(\frac{x \left(3 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{\cot{\left(x \right)}}{x}\right)}{\log{\left(x \right)} \cot{\left(x \right)}} + \frac{2 x \left(40 x^{4} \sqrt[3]{2 - 3 x} - \frac{x^{5} + 9}{\left(2 - 3 x\right)^{\frac{2}{3}}}\right)}{\sqrt[3]{2 - 3 x} \left(x^{5} + 9\right)} - 2\right)}{x^{2}}\right)}{18}$$
Gráfico