Mister Exam
Other calculators
- Derivative of a implicit defined function
- Derivative of Parametric Function
- Partial derivative of the function
- Curve tracing functions Step by Step
- Integral Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Derivative of:
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Derivative of 3*sqrt(x)
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Derivative of 2*y
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Derivative of 2^x+1
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Derivative of (2x-1)^3
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Identical expressions
- arctg(x+cosx)
- arctg(x plus co sinus of e of x)
- arctgx+cosx
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Similar expressions
- arctg(x-cosx)
Derivative of arctg(x+cosx)
The solution
You have entered
[src]
atan(x + cos(x))
$$\operatorname{atan}{\left(x + \cos{\left(x \right)} \right)}$$
atan(x + cos(x))
The first derivative
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1 - sin(x)
-----------------
2
1 + (x + cos(x))
$$\frac{1 - \sin{\left(x \right)}}{\left(x + \cos{\left(x \right)}\right)^{2} + 1}$$
The second derivative
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/ 2 \
|2*(-1 + sin(x)) *(x + cos(x)) |
-|----------------------------- + cos(x)|
| 2 |
\ 1 + (x + cos(x)) /
------------------------------------------
2
1 + (x + cos(x))
$$- \frac{\frac{2 \left(x + \cos{\left(x \right)}\right) \left(\sin{\left(x \right)} - 1\right)^{2}}{\left(x + \cos{\left(x \right)}\right)^{2} + 1} + \cos{\left(x \right)}}{\left(x + \cos{\left(x \right)}\right)^{2} + 1}$$
The third derivative
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3 3 2
2*(-1 + sin(x)) 8*(-1 + sin(x)) *(x + cos(x)) 6*(-1 + sin(x))*(x + cos(x))*cos(x)
----------------- - ------------------------------ - ----------------------------------- + sin(x)
2 2 2
1 + (x + cos(x)) / 2\ 1 + (x + cos(x))
\1 + (x + cos(x)) /
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2
1 + (x + cos(x))
$$\frac{- \frac{8 \left(x + \cos{\left(x \right)}\right)^{2} \left(\sin{\left(x \right)} - 1\right)^{3}}{\left(\left(x + \cos{\left(x \right)}\right)^{2} + 1\right)^{2}} - \frac{6 \left(x + \cos{\left(x \right)}\right) \left(\sin{\left(x \right)} - 1\right) \cos{\left(x \right)}}{\left(x + \cos{\left(x \right)}\right)^{2} + 1} + \sin{\left(x \right)} + \frac{2 \left(\sin{\left(x \right)} - 1\right)^{3}}{\left(x + \cos{\left(x \right)}\right)^{2} + 1}}{\left(x + \cos{\left(x \right)}\right)^{2} + 1}$$
The graph