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The derivative of the function/ (acos2x+bsin2x)

Derivative of (acos2x+bsin2x)

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

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The solution

You have entered [src] 
acos(2*x) + b*sin(2*x)
$$b \sin{\left(2 x \right)} + \operatorname{acos}{\left(2 x \right)}$$ 
d                         
--(acos(2*x) + b*sin(2*x))
dx
$$\frac{\partial}{\partial x} \left(b \sin{\left(2 x \right)} + \operatorname{acos}{\left(2 x \right)}\right)$$
Transform
The first derivative [src] 
        2                     
- ------------- + 2*b*cos(2*x)
     __________               
    /        2                
  \/  1 - 4*x
$$2 b \cos{\left(2 x \right)} - \frac{2}{\sqrt{1 - 4 x^{2}}}$$
Simplify
The second derivative [src] 
   /                  2*x     \
-4*|b*sin(2*x) + -------------|
   |                       3/2|
   |             /       2\   |
   \             \1 - 4*x /   /
$$- 4 \left(b \sin{\left(2 x \right)} + \frac{2 x}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right)$$
Simplify
The third derivative [src] 
   /                                     2    \
   |      1                          12*x     |
-8*|------------- + b*cos(2*x) + -------------|
   |          3/2                          5/2|
   |/       2\                   /       2\   |
   \\1 - 4*x /                   \1 - 4*x /   /
$$- 8 \left(b \cos{\left(2 x \right)} + \frac{12 x^{2}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} + \frac{1}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right)$$
Simplify
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