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- Derivative of:
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Derivative of |x-1|
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Derivative of sin(x)*cos(x)+x
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Derivative of sin(3*x)^(2)
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Derivative of log(x)*cos(x)
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Identical expressions
- arccossqrt(x)*sinx^ two *e^cos2x
- arc co sinus of e of square root of (x) multiply by sinus of x squared multiply by e to the power of co sinus of e of 2x
- arc co sinus of e of square root of (x) multiply by sinus of x to the power of two multiply by e to the power of co sinus of e of 2x
- arccos√(x)*sinx^2*e^cos2x
- arccossqrt(x)*sinx2*ecos2x
- arccossqrtx*sinx2*ecos2x
- arccossqrt(x)*sinx²*e^cos2x
- arccossqrt(x)*sinx to the power of 2*e to the power of cos2x
- arccossqrt(x)sinx^2e^cos2x
- arccossqrt(x)sinx2ecos2x
- arccossqrtxsinx2ecos2x
- arccossqrtxsinx^2e^cos2x
Derivative of arccossqrt(x)*sinx^2*e^cos2x
The solution
You have entered
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/ ___\ 2 cos(2*x) acos\\/ x /*sin (x)*E
$$e^{\cos{\left(2 x \right)}} \sin^{2}{\left(x \right)} \operatorname{acos}{\left(\sqrt{x} \right)}$$
(acos(sqrt(x))*sin(x)^2)*E^cos(2*x)
The first derivative
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/ 2 \ | / ___\ sin (x) | cos(2*x) 2 / ___\ cos(2*x) |2*acos\\/ x /*cos(x)*sin(x) - -----------------|*e - 2*sin (x)*acos\\/ x /*e *sin(2*x) | ___ _______| \ 2*\/ x *\/ 1 - x /
$$\left(2 \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{acos}{\left(\sqrt{x} \right)} - \frac{\sin^{2}{\left(x \right)}}{2 \sqrt{x} \sqrt{1 - x}}\right) e^{\cos{\left(2 x \right)}} - 2 e^{\cos{\left(2 x \right)}} \sin^{2}{\left(x \right)} \sin{\left(2 x \right)} \operatorname{acos}{\left(\sqrt{x} \right)}$$
The second derivative
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/ 2 /1 1 \\ | sin (x)*|- + ------|| | / 2 2 \ / ___\ / / ___\ sin(x) \ 2 / 2 \ / ___\ 2*cos(x)*sin(x) \x -1 + x/| cos(2*x) |- 2*\sin (x) - cos (x)/*acos\\/ x / - 2*|4*acos\\/ x /*cos(x) - ---------------|*sin(x)*sin(2*x) + 4*sin (x)*\sin (2*x) - cos(2*x)/*acos\\/ x / - --------------- + --------------------|*e | | ___ _______| ___ _______ ___ _______ | \ \ \/ x *\/ 1 - x / \/ x *\/ 1 - x 4*\/ x *\/ 1 - x /
$$\left(- 2 \left(4 \cos{\left(x \right)} \operatorname{acos}{\left(\sqrt{x} \right)} - \frac{\sin{\left(x \right)}}{\sqrt{x} \sqrt{1 - x}}\right) \sin{\left(x \right)} \sin{\left(2 x \right)} - 2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{acos}{\left(\sqrt{x} \right)} + 4 \left(\sin^{2}{\left(2 x \right)} - \cos{\left(2 x \right)}\right) \sin^{2}{\left(x \right)} \operatorname{acos}{\left(\sqrt{x} \right)} + \frac{\left(\frac{1}{x - 1} + \frac{1}{x}\right) \sin^{2}{\left(x \right)}}{4 \sqrt{x} \sqrt{1 - x}} - \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{x} \sqrt{1 - x}}\right) e^{\cos{\left(2 x \right)}}$$
The third derivative
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/ / 2 /1 1 \ \ \ | | sin (x)*|- + ------| | | | | / 2 2 \ / ___\ \x -1 + x/ 8*cos(x)*sin(x)| 2 /3 3 2 \ | |3*|8*\sin (x) - cos (x)/*acos\\/ x / - -------------------- + ---------------|*sin(2*x) sin (x)*|-- + --------- + ----------| /1 1 \ | | | ___ _______ ___ _______| / 2 2 \ | 2 2 x*(-1 + x)| 3*|- + ------|*cos(x)*sin(x)| | \ \/ x *\/ 1 - x \/ x *\/ 1 - x / / ___\ 3*\sin (x) - cos (x)/ / 2 \ / / ___\ sin(x) \ 2 / 2 \ / ___\ \x (-1 + x) / \x -1 + x/ | cos(2*x) |--------------------------------------------------------------------------------------- - 8*acos\\/ x /*cos(x)*sin(x) + --------------------- + 6*\sin (2*x) - cos(2*x)/*|4*acos\\/ x /*cos(x) - ---------------|*sin(x) + 8*sin (x)*\1 - sin (2*x) + 3*cos(2*x)/*acos\\/ x /*sin(2*x) - ------------------------------------- + ----------------------------|*e | 2 ___ _______ | ___ _______| ___ _______ ___ _______ | \ \/ x *\/ 1 - x \ \/ x *\/ 1 - x / 8*\/ x *\/ 1 - x 2*\/ x *\/ 1 - x /
$$\left(6 \left(4 \cos{\left(x \right)} \operatorname{acos}{\left(\sqrt{x} \right)} - \frac{\sin{\left(x \right)}}{\sqrt{x} \sqrt{1 - x}}\right) \left(\sin^{2}{\left(2 x \right)} - \cos{\left(2 x \right)}\right) \sin{\left(x \right)} + \frac{3 \left(8 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) \operatorname{acos}{\left(\sqrt{x} \right)} - \frac{\left(\frac{1}{x - 1} + \frac{1}{x}\right) \sin^{2}{\left(x \right)}}{\sqrt{x} \sqrt{1 - x}} + \frac{8 \sin{\left(x \right)} \cos{\left(x \right)}}{\sqrt{x} \sqrt{1 - x}}\right) \sin{\left(2 x \right)}}{2} + 8 \left(- \sin^{2}{\left(2 x \right)} + 3 \cos{\left(2 x \right)} + 1\right) \sin^{2}{\left(x \right)} \sin{\left(2 x \right)} \operatorname{acos}{\left(\sqrt{x} \right)} - 8 \sin{\left(x \right)} \cos{\left(x \right)} \operatorname{acos}{\left(\sqrt{x} \right)} + \frac{3 \left(\frac{1}{x - 1} + \frac{1}{x}\right) \sin{\left(x \right)} \cos{\left(x \right)}}{2 \sqrt{x} \sqrt{1 - x}} + \frac{3 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)}{\sqrt{x} \sqrt{1 - x}} - \frac{\left(\frac{3}{\left(x - 1\right)^{2}} + \frac{2}{x \left(x - 1\right)} + \frac{3}{x^{2}}\right) \sin^{2}{\left(x \right)}}{8 \sqrt{x} \sqrt{1 - x}}\right) e^{\cos{\left(2 x \right)}}$$