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 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
- Graphing y =:
- sin(x)*atan(x)
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Identical expressions
- sin(x)*atan(x)
- sinus of (x) multiply by arc tangent of gent of (x)
- sin(x)atan(x)
- sinxatanx
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Similar expressions
- sin(x)*arctan(x)
- sinx*arctanx
Derivative of sin(x)*atan(x)
The solution
You have entered
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sin(x)*atan(x)
$$\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}$$
sin(x)*atan(x)
The first derivative
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sin(x)
------ + atan(x)*cos(x)
2
1 + x
$$\cos{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin{\left(x \right)}}{x^{2} + 1}$$
The second derivative
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2*cos(x) 2*x*sin(x)
-atan(x)*sin(x) + -------- - ----------
2 2
1 + x / 2\
\1 + x /
$$- \frac{2 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x^{2} + 1}$$
The third derivative
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/ 2 \
| 4*x |
2*|-1 + ------|*sin(x)
| 2|
3*sin(x) 6*x*cos(x) \ 1 + x /
-atan(x)*cos(x) - -------- - ---------- + ----------------------
2 2 2
1 + x / 2\ / 2\
\1 + x / \1 + x /
$$- \frac{6 x \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x^{2} + 1} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}$$
The graph