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- Derivada de una función implícitamente dada
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- Análisis de la función gráfica
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- Derivada de:
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Derivada de x^(7/6)
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Derivada de x^-7
- Derivada de i*n*x
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Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
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Expresiones idénticas
- (x*(x- tres)^ dos)^(uno / tres)x*exp(-x)
- (x multiplicar por (x menos 3) al cuadrado ) en el grado (1 dividir por 3)x multiplicar por exponente de ( menos x)
- (x multiplicar por (x menos tres) en el grado dos) en el grado (uno dividir por tres)x multiplicar por exponente de ( menos x)
- (x*(x-3)2)(1/3)x*exp(-x)
- x*x-321/3x*exp-x
- (x*(x-3)²)^(1/3)x*exp(-x)
- (x*(x-3) en el grado 2) en el grado (1/3)x*exp(-x)
- (x(x-3)^2)^(1/3)xexp(-x)
- (x(x-3)2)(1/3)xexp(-x)
- xx-321/3xexp-x
- xx-3^2^1/3xexp-x
- (x*(x-3)^2)^(1 dividir por 3)x*exp(-x)
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Expresiones semejantes
- (x*(x-3)^2)^(1/3)x*exp(x)
- (x*(x+3)^2)^(1/3)x*exp(-x)
Derivada de (x*(x-3)^2)^(1/3)x*exp(-x)
Solución
Ha introducido
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____________ 3 / 2 -x \/ x*(x - 3) *x*e
$$x \sqrt[3]{x \left(x - 3\right)^{2}} e^{- x}$$
((x*(x - 3)^2)^(1/3)*x)*exp(-x)
Primera derivada
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/ / 2 \\ | 3 ___ 2/3 |(x - 3) x*(-6 + 2*x)|| | ____________ \/ x *|x - 3| *|-------- + ------------|| |3 / 2 \ 3 3 /| -x 3 ___ 2/3 -x |\/ x*(x - 3) + ------------------------------------------|*e - x*\/ x *|x - 3| *e | 2 | \ (x - 3) /
$$- x \sqrt[3]{x} \left|{x - 3}\right|^{\frac{2}{3}} e^{- x} + \left(\frac{\sqrt[3]{x} \left(\frac{x \left(2 x - 6\right)}{3} + \frac{\left(x - 3\right)^{2}}{3}\right) \left|{x - 3}\right|^{\frac{2}{3}}}{\left(x - 3\right)^{2}} + \sqrt[3]{x \left(x - 3\right)^{2}}\right) e^{- x}$$
Segunda derivada
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/ / / 2/3 3 ___ \ \ \ | | ||-3 + x| 2*\/ x *sign(-3 + x)| | | | |(-1 + x)*|----------- + --------------------| | | | | | 2/3 3 __________ | 2/3 2/3 2/3 | 2/3 | | | \ x \/ |-3 + x| / 3*|-3 + x| *(-1 + x) 6*|-3 + x| *(-1 + x) 6*|-3 + x| *(-2 + x)| 6*|-3 + x| *(-1 + x) | | x*|--------------------------------------------- - ---------------------- - ---------------------- + ----------------------| + ---------------------- | | | x 5/3 2/3 2/3 | 2/3 | | 4/3 2/3 \ x x *(-3 + x) x *(-3 + x) / x 3 ___ 2/3 / -1 + x\| -x |x *|-3 + x| + ----------------------------------------------------------------------------------------------------------------------------------------------------- - 2*\/ x *|-3 + x| *|1 + ------||*e \ 3*(-3 + x) \ -3 + x//
$$\left(x^{\frac{4}{3}} \left|{x - 3}\right|^{\frac{2}{3}} - 2 \sqrt[3]{x} \left(1 + \frac{x - 1}{x - 3}\right) \left|{x - 3}\right|^{\frac{2}{3}} + \frac{x \left(\frac{\left(x - 1\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x} + \frac{6 \left(x - 2\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{6 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{3 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}}}\right) + \frac{6 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}}{3 \left(x - 3\right)}\right) e^{- x}$$
Tercera derivada
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/ / / 2/3 3 ___ \ \ / / 2/3 3 ___ \ / 2/3 3 ___ 2 3 ___ \ / 2/3 3 ___ \ / 2/3 3 ___ \ \ / 2/3 3 ___ \ \ | | ||-3 + x| 2*\/ x *sign(-3 + x)| | | ||-3 + x| 2*\/ x *sign(-3 + x)| | |-3 + x| \/ x *sign (-3 + x) 2*sign(-3 + x) 6*\/ x *DiracDelta(-3 + x)| ||-3 + x| 2*\/ x *sign(-3 + x)| ||-3 + x| 2*\/ x *sign(-3 + x)| | ||-3 + x| 2*\/ x *sign(-3 + x)| | | |(-1 + x)*|----------- + --------------------| | | 3*(-1 + x)*|----------- + --------------------| 2*(-1 + x)*|- ----------- - ------------------- + ----------------- + --------------------------| 6*(-1 + x)*|----------- + --------------------| 6*(-2 + x)*|----------- + --------------------| | 9*(-1 + x)*|----------- + --------------------| | | | | 2/3 3 __________ | 2/3 2/3 2/3 | 2/3 | | 2/3 3 __________ | | 5/3 4/3 2/3 3 __________ 3 __________ | 2/3 2/3 2/3 2/3 | 2/3 3 __________ | | 2/3 3 __________ | 2/3 2/3 | 2/3 | 2/3 3 __________ | 2/3 2/3 | | | \ x \/ |-3 + x| / 3*|-3 + x| *(-1 + x) 6*|-3 + x| *(-1 + x) 6*|-3 + x| *(-2 + x)| 6*|-3 + x| *(-1 + x) | \ x \/ |-3 + x| / \ x |-3 + x| x *\/ |-3 + x| \/ |-3 + x| / 15*|-3 + x| *(-1 + x) 18*|-3 + x| 72*|-3 + x| *(-2 + x) 30*|-3 + x| *(-2 + x) \ x \/ |-3 + x| / 6*(-1 + x)*sign(-3 + x) \ x \/ |-3 + x| / 30*|-3 + x| *(-1 + x) 54*|-3 + x| *(-1 + x) 12*(-1 + x)*sign(-3 + x) 12*(-2 + x)*sign(-3 + x) | 27*|-3 + x| *(-1 + x) \ x \/ |-3 + x| / 54*|-3 + x| *(-1 + x) 54*|-3 + x| *(-2 + x) | | x*|--------------------------------------------- - ---------------------- - ---------------------- + ----------------------| + ---------------------- x*|- ----------------------------------------------- + ------------------------------------------------------------------------------------------------- + ----------------------- + -------------- - ----------------------- - ----------------------- - ----------------------------------------------- - ----------------------- + ----------------------------------------------- + ----------------------- + ----------------------- - -------------------------- + --------------------------| - ----------------------- + ----------------------------------------------- - ----------------------- + ----------------------- | | | x 5/3 2/3 2/3 | 2/3 | 2 x 8/3 2/3 2/3 2 5/3 x*(-3 + x) 5/3 3 __________ x*(-3 + x) 5/3 2/3 2 2/3 3 __________ 2/3 3 __________| 5/3 x 2/3 2/3 | | 4/3 2/3 \ x x *(-3 + x) x *(-3 + x) / x \ x x x *(-3 + x) x *(-3 + x) x *(-3 + x) x *\/ |-3 + x| x *(-3 + x) x *(-3 + x) x *(-3 + x)*\/ |-3 + x| x *(-3 + x)*\/ |-3 + x| / x x *(-3 + x) x *(-3 + x) 3 ___ 2/3 / -1 + x\| -x |- x *|-3 + x| - ----------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + 3*\/ x *|-3 + x| *|1 + ------||*e \ -3 + x 9*(-3 + x) \ -3 + x//
$$\left(- x^{\frac{4}{3}} \left|{x - 3}\right|^{\frac{2}{3}} + 3 \sqrt[3]{x} \left(1 + \frac{x - 1}{x - 3}\right) \left|{x - 3}\right|^{\frac{2}{3}} - \frac{x \left(\frac{\left(x - 1\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x} + \frac{6 \left(x - 2\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{6 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{3 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}}}\right) + \frac{6 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}}{x - 3} + \frac{x \left(\frac{2 \left(x - 1\right) \left(\frac{6 \sqrt[3]{x} \delta\left(x - 3\right)}{\sqrt[3]{\left|{x - 3}\right|}} - \frac{\sqrt[3]{x} \operatorname{sign}^{2}{\left(x - 3 \right)}}{\left|{x - 3}\right|^{\frac{4}{3}}} + \frac{2 \operatorname{sign}{\left(x - 3 \right)}}{x^{\frac{2}{3}} \sqrt[3]{\left|{x - 3}\right|}} - \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}}}\right)}{x} + \frac{6 \left(x - 2\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x \left(x - 3\right)} - \frac{6 \left(x - 1\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x \left(x - 3\right)} - \frac{3 \left(x - 1\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x^{2}} + \frac{12 \left(x - 2\right) \operatorname{sign}{\left(x - 3 \right)}}{x^{\frac{2}{3}} \left(x - 3\right) \sqrt[3]{\left|{x - 3}\right|}} - \frac{12 \left(x - 1\right) \operatorname{sign}{\left(x - 3 \right)}}{x^{\frac{2}{3}} \left(x - 3\right) \sqrt[3]{\left|{x - 3}\right|}} + \frac{18 \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{72 \left(x - 2\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)^{2}} + \frac{54 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)^{2}} - \frac{6 \left(x - 1\right) \operatorname{sign}{\left(x - 3 \right)}}{x^{\frac{5}{3}} \sqrt[3]{\left|{x - 3}\right|}} - \frac{30 \left(x - 2\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}} \left(x - 3\right)} + \frac{30 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}} \left(x - 3\right)} + \frac{15 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{8}{3}}}\right) + \frac{9 \left(x - 1\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x} + \frac{54 \left(x - 2\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{54 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{27 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}}}}{9 \left(x - 3\right)}\right) e^{- x}$$