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x^4-1/5*cos(x)^(5)+2
The derivative of the function/ x^4-1/5*cos(x)^(5)+2

Derivative of x^4-1/5*cos(x)^(5)+2

Function f() - derivative -N order at the point
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The graph:

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Piecewise:

The solution

You have entered [src] 
        5       
 4   cos (x)    
x  - ------- + 2
        5
$$- \frac{\cos^{5}{\left(x \right)}}{5} + x^{4} + 2$$ 
  /        5       \
d | 4   cos (x)    |
--|x  - ------- + 2|
dx\        5       /
$$\frac{d}{d x} \left(- \frac{\cos^{5}{\left(x \right)}}{5} + x^{4} + 2\right)$$
Transform
Detail solution

  1. Differentiate term by term:

    1. Apply the power rule: goes to

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Let .

        2. Apply the power rule: goes to

        3. Then, apply the chain rule. Multiply by :

          1. The derivative of cosine is negative sine:

          The result of the chain rule is:

        So, the result is:

      So, the result is:

    3. The derivative of the constant is zero.

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
   3      4          
4*x  + cos (x)*sin(x)
$$\sin{\left(x \right)} \cos^{4}{\left(x \right)} + 4 x^{3}$$
Simplify
The second derivative [src] 
   5          2        3       2   
cos (x) + 12*x  - 4*cos (x)*sin (x)
$$- 4 \sin^{2}{\left(x \right)} \cos^{3}{\left(x \right)} + \cos^{5}{\left(x \right)} + 12 x^{2}$$
Simplify
The third derivative [src] 
             4                   2       3   
24*x - 13*cos (x)*sin(x) + 12*cos (x)*sin (x)
$$12 \sin^{3}{\left(x \right)} \cos^{2}{\left(x \right)} - 13 \sin{\left(x \right)} \cos^{4}{\left(x \right)} + 24 x$$
Simplify
The graph
Derivative of x^4-1/5*cos(x)^(5)+2
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