Mister Exam
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- 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 x/(e^x+1)
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Derivative of (x^2-1)/((2*x))
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Derivative of sqrt(x)^2-2*x
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Derivative of sin(4*x-1)^(3)
- Limit of the function:
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atan(sin(x))
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Identical expressions
- atan(sin(x))
- arc tangent of gent of ( sinus of (x))
- atansinx
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Similar expressions
- atan((sin(x)+cos(x))/(sin(x)-cos(x)))
- arctan(sin(x))
- atan(sinx)
Derivative of atan(sin(x))
The solution
You have entered
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atan(sin(x))
$$\operatorname{atan}{\left(\sin{\left(x \right)} \right)}$$
atan(sin(x))
The first derivative
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cos(x)
-----------
2
1 + sin (x)
$$\frac{\cos{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}$$
The second derivative
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/ 2 \
| 2*cos (x) |
-|1 + -----------|*sin(x)
| 2 |
\ 1 + sin (x)/
--------------------------
2
1 + sin (x)
$$- \frac{\left(1 + \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}\right) \sin{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}$$
The third derivative
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/ 2 2 2 2 \
| 2*cos (x) 6*sin (x) 8*cos (x)*sin (x)|
|-1 - ----------- + ----------- + -----------------|*cos(x)
| 2 2 2 |
| 1 + sin (x) 1 + sin (x) / 2 \ |
\ \1 + sin (x)/ /
-----------------------------------------------------------
2
1 + sin (x)
$$\frac{\left(-1 + \frac{6 \sin^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} - \frac{2 \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1} + \frac{8 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}{\left(\sin^{2}{\left(x \right)} + 1\right)^{2}}\right) \cos{\left(x \right)}}{\sin^{2}{\left(x \right)} + 1}$$
The graph