Mister Exam
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- Derivative of a implicit defined function
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- Partial derivative of the function
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How to use it?
- Derivative of:
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Derivative of sqrt(4-x^2)
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Derivative of 5x
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Derivative of asin(sqrt(x))
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Derivative of 1/(x-1)
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Identical expressions
- (cos(2x))*atan(x)
- ( co sinus of e of (2x)) multiply by arc tangent of gent of (x)
- (cos(2x))atan(x)
- cos2xatanx
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Similar expressions
- (cos(2x))*arctan(x)
- (cos(2x))*arctanx
Derivative of (cos(2x))*atan(x)
The solution
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cos(2*x)*atan(x)
$$\cos{\left(2 x \right)} \operatorname{atan}{\left(x \right)}$$
d --(cos(2*x)*atan(x)) dx
$$\frac{d}{d x} \cos{\left(2 x \right)} \operatorname{atan}{\left(x \right)}$$
The first derivative
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cos(2*x)
-------- - 2*atan(x)*sin(2*x)
2
1 + x
$$- 2 \sin{\left(2 x \right)} \operatorname{atan}{\left(x \right)} + \frac{\cos{\left(2 x \right)}}{x^{2} + 1}$$
The second derivative
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/2*sin(2*x) x*cos(2*x)\ -2*|---------- + 2*atan(x)*cos(2*x) + ----------| | 2 2 | | 1 + x / 2\ | \ \1 + x / /
$$- 2 \left(\frac{x \cos{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + 2 \cos{\left(2 x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \sin{\left(2 x \right)}}{x^{2} + 1}\right)$$
The third derivative
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/ / 2 \ \ | | 4*x | | | |-1 + ------|*cos(2*x) | | | 2| | | 6*cos(2*x) \ 1 + x / 6*x*sin(2*x)| 2*|- ---------- + 4*atan(x)*sin(2*x) + ---------------------- + ------------| | 2 2 2 | | 1 + x / 2\ / 2\ | \ \1 + x / \1 + x / /
$$2 \cdot \left(\frac{6 x \sin{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}} + 4 \sin{\left(2 x \right)} \operatorname{atan}{\left(x \right)} - \frac{6 \cos{\left(2 x \right)}}{x^{2} + 1} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \cos{\left(2 x \right)}}{\left(x^{2} + 1\right)^{2}}\right)$$
The graph