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How to use it?
- Derivative of:
- Derivative of e^x^x
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Derivative of x/(x-4)
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Derivative of tan(e^(2*x))
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Derivative of sin^3*x
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Identical expressions
- (arctan(2x)+ three)sin(cosx)
- (arc tangent of (2x) plus 3) sinus of ( co sinus of e of x)
- (arc tangent of (2x) plus three) sinus of ( co sinus of e of x)
- arctan2x+3sincosx
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Similar expressions
- (arctan(2x)-3)sin(cosx)
Derivative of (arctan(2x)+3)sin(cosx)
The solution
You have entered
[src]
(atan(2*x) + 3)*sin(cos(x))
$$\left(\operatorname{atan}{\left(2 x \right)} + 3\right) \sin{\left(\cos{\left(x \right)} \right)}$$
(atan(2*x) + 3)*sin(cos(x))
The first derivative
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2*sin(cos(x))
------------- - (atan(2*x) + 3)*cos(cos(x))*sin(x)
2
1 + 4*x
$$- \left(\operatorname{atan}{\left(2 x \right)} + 3\right) \sin{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} + \frac{2 \sin{\left(\cos{\left(x \right)} \right)}}{4 x^{2} + 1}$$
The second derivative
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/ / 2 \ 4*cos(cos(x))*sin(x) 16*x*sin(cos(x))\ -|(3 + atan(2*x))*\sin (x)*sin(cos(x)) + cos(x)*cos(cos(x))/ + -------------------- + ----------------| | 2 2 | | 1 + 4*x / 2\ | \ \1 + 4*x / /
$$- (\frac{16 x \sin{\left(\cos{\left(x \right)} \right)}}{\left(4 x^{2} + 1\right)^{2}} + \left(\sin^{2}{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)} + \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)}\right) \left(\operatorname{atan}{\left(2 x \right)} + 3\right) + \frac{4 \sin{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)}}{4 x^{2} + 1})$$
The third derivative
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/ 2 \
| 16*x |
16*|-1 + --------|*sin(cos(x))
/ 2 \ | 2|
6*\sin (x)*sin(cos(x)) + cos(x)*cos(cos(x))/ / 2 \ \ 1 + 4*x / 48*x*cos(cos(x))*sin(x)
- -------------------------------------------- + (3 + atan(2*x))*\sin (x)*cos(cos(x)) - 3*cos(x)*sin(cos(x)) + cos(cos(x))/*sin(x) + ------------------------------ + -----------------------
2 2 2
1 + 4*x / 2\ / 2\
\1 + 4*x / \1 + 4*x /
$$\frac{48 x \sin{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)}}{\left(4 x^{2} + 1\right)^{2}} + \left(\operatorname{atan}{\left(2 x \right)} + 3\right) \left(\sin^{2}{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)} - 3 \sin{\left(\cos{\left(x \right)} \right)} \cos{\left(x \right)} + \cos{\left(\cos{\left(x \right)} \right)}\right) \sin{\left(x \right)} - \frac{6 \left(\sin^{2}{\left(x \right)} \sin{\left(\cos{\left(x \right)} \right)} + \cos{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)}\right)}{4 x^{2} + 1} + \frac{16 \left(\frac{16 x^{2}}{4 x^{2} + 1} - 1\right) \sin{\left(\cos{\left(x \right)} \right)}}{\left(4 x^{2} + 1\right)^{2}}$$