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The derivative of the function/ -3(cos^(1/3)x)

Derivative of -3(cos^(1/3)x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   3 ________
-3*\/ cos(x)
$$- 3 \sqrt[3]{\cos{\left(x \right)}}$$ 
-3*cos(x)^(1/3)
Detail solution

  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:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  sin(x) 
---------
   2/3   
cos   (x)
$$\frac{\sin{\left(x \right)}}{\cos^{\frac{2}{3}}{\left(x \right)}}$$
Simplify
The second derivative [src] 
                   2    
3 ________    2*sin (x) 
\/ cos(x)  + -----------
                  5/3   
             3*cos   (x)
$$\frac{2 \sin^{2}{\left(x \right)}}{3 \cos^{\frac{5}{3}}{\left(x \right)}} + \sqrt[3]{\cos{\left(x \right)}}$$
Simplify
The third derivative [src] 
/          2   \       
|    10*sin (x)|       
|9 + ----------|*sin(x)
|        2     |       
\     cos (x)  /       
-----------------------
           2/3         
      9*cos   (x)
$$\frac{\left(\frac{10 \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 9\right) \sin{\left(x \right)}}{9 \cos^{\frac{2}{3}}{\left(x \right)}}$$
Simplify
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