Mister Exam

Other calculators

(arctan(2x)+3)*sin(cosx)
The derivative of the function/ (arctan(2x)+3)*sin(cosx)

Derivative of (arctan(2x)+3)*sin(cosx)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
(atan(2*x) + 3)*sin(cos(x))
(atan⁡(2x)+3)sin⁡(cos⁡(x))\left(\operatorname{atan}{\left(2 x \right)} + 3\right) \sin{\left(\cos{\left(x \right)} \right)} 
d                              
--((atan(2*x) + 3)*sin(cos(x)))
dx
ddx(atan⁡(2x)+3)sin⁡(cos⁡(x))\frac{d}{d x} \left(\operatorname{atan}{\left(2 x \right)} + 3\right) \sin{\left(\cos{\left(x \right)} \right)}
Transform
The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
2*sin(cos(x))                                     
------------- - (atan(2*x) + 3)*cos(cos(x))*sin(x)
          2                                       
   1 + 4*x
−(atan⁡(2x)+3)sin⁡(x)cos⁡(cos⁡(x))+2sin⁡(cos⁡(x))4x2+1- \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}
Simplify
The second derivative [src] 
 /                /   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 /    /
−((sin⁡2(x)sin⁡(cos⁡(x))+cos⁡(x)cos⁡(cos⁡(x)))(atan⁡(2x)+3)+4sin⁡(x)cos⁡(cos⁡(x))4x2+1+16xsin⁡(cos⁡(x))(4x2+1)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} + \frac{16 x \sin{\left(\cos{\left(x \right)} \right)}}{\left(4 x^{2} + 1\right)^{2}})
Simplify
The third derivative [src] 
                                                                                                                                        /          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 /
(atan⁡(2x)+3)(sin⁡2(x)cos⁡(cos⁡(x))−3sin⁡(cos⁡(x))cos⁡(x)+cos⁡(cos⁡(x)))sin⁡(x)+48xsin⁡(x)cos⁡(cos⁡(x))(4x2+1)2−6(sin⁡2(x)sin⁡(cos⁡(x))+cos⁡(x)cos⁡(cos⁡(x)))4x2+1+16⋅(16x24x2+1−1)sin⁡(cos⁡(x))(4x2+1)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{48 x \sin{\left(x \right)} \cos{\left(\cos{\left(x \right)} \right)}}{\left(4 x^{2} + 1\right)^{2}} - \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 \cdot \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}}
Simplify
The graph
Derivative of (arctan(2x)+3)*sin(cosx)
    © Mister Exam – Calculator