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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 2*sin(x)*cos(x)
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Derivative of x^(1/4)
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Derivative of 9
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Derivative of log(sin(x))
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Identical expressions
- y= two ^x*arctg3x
- y equally 2 to the power of x multiply by arctg3x
- y equally two to the power of x multiply by arctg3x
- y=2x*arctg3x
- y=2^xarctg3x
- y=2xarctg3x
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Similar expressions
- y=2^xarctg3x
Derivative of y=2^x*arctg3x
The solution
You have entered
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x 2 *atan(3*x)
$$2^{x} \operatorname{atan}{\left(3 x \right)}$$
2^x*atan(3*x)
The first derivative
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x
3*2 x
-------- + 2 *atan(3*x)*log(2)
2
1 + 9*x
$$2^{x} \log{\left(2 \right)} \operatorname{atan}{\left(3 x \right)} + \frac{3 \cdot 2^{x}}{9 x^{2} + 1}$$
The second derivative
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x / 2 54*x 6*log(2)\ 2 *|log (2)*atan(3*x) - ----------- + --------| | 2 2| | / 2\ 1 + 9*x | \ \1 + 9*x / /
$$2^{x} \left(- \frac{54 x}{\left(9 x^{2} + 1\right)^{2}} + \log{\left(2 \right)}^{2} \operatorname{atan}{\left(3 x \right)} + \frac{6 \log{\left(2 \right)}}{9 x^{2} + 1}\right)$$
The third derivative
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/ / 2 \ \ | | 36*x | | | 54*|-1 + --------| | | 2 | 2| | x | 3 9*log (2) \ 1 + 9*x / 162*x*log(2)| 2 *|log (2)*atan(3*x) + --------- + ------------------ - ------------| | 2 2 2 | | 1 + 9*x / 2\ / 2\ | \ \1 + 9*x / \1 + 9*x / /
$$2^{x} \left(- \frac{162 x \log{\left(2 \right)}}{\left(9 x^{2} + 1\right)^{2}} + \log{\left(2 \right)}^{3} \operatorname{atan}{\left(3 x \right)} + \frac{9 \log{\left(2 \right)}^{2}}{9 x^{2} + 1} + \frac{54 \left(\frac{36 x^{2}}{9 x^{2} + 1} - 1\right)}{\left(9 x^{2} + 1\right)^{2}}\right)$$