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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of sqrt(cos(x))
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Derivative of cos(2t)
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Derivative of 5*tan(x)
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Derivative of 3xsinx
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Identical expressions
- five *sin*(x)*arctg*(x)
- 5 multiply by sinus of multiply by (x) multiply by arctg multiply by (x)
- five multiply by sinus of multiply by (x) multiply by arctg multiply by (x)
- 5sin(x)arctg(x)
- 5sinxarctgx
Derivative of 5*sin*(x)*arctg*(x)
The solution
You have entered
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5*sin(x)*atan(x)
$$5 \sin{\left(x \right)} \operatorname{atan}{\left(x \right)}$$
(5*sin(x))*atan(x)
The first derivative
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5*sin(x)
-------- + 5*atan(x)*cos(x)
2
1 + x
$$5 \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{5 \sin{\left(x \right)}}{x^{2} + 1}$$
The second derivative
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/ 2*cos(x) 2*x*sin(x)\ 5*|-atan(x)*sin(x) + -------- - ----------| | 2 2 | | 1 + x / 2\ | \ \1 + x / /
$$5 \left(- \frac{2 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x^{2} + 1}\right)$$
The third derivative
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/ / 2 \ \ | | 4*x | | | 2*|-1 + ------|*sin(x)| | | 2| | | 3*sin(x) 6*x*cos(x) \ 1 + x / | 5*|-atan(x)*cos(x) - -------- - ---------- + ----------------------| | 2 2 2 | | 1 + x / 2\ / 2\ | \ \1 + x / \1 + x / /
$$5 \left(- \frac{6 x \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x^{2} + 1} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)$$