Mister Exam

Other calculators

  • How to use it?

  • Derivative of:
  • Derivative of 9/x Derivative of 9/x
  • Derivative of x^-5 Derivative of x^-5
  • Derivative of x^-3 Derivative of x^-3
  • Derivative of x^2*e^x Derivative of x^2*e^x

  • Identical expressions

  • -(x/ four *cosx)+(four /x^ two *sinx)
  • minus (x divide by 4 multiply by co sinus of e of x) plus (4 divide by x squared multiply by sinus of x)
  • minus (x divide by four multiply by co sinus of e of x) plus (four divide by x to the power of two multiply by sinus of x)
  • -(x/4*cosx)+(4/x2*sinx)
  • -x/4*cosx+4/x2*sinx
  • -(x/4*cosx)+(4/x²*sinx)
  • -(x/4*cosx)+(4/x to the power of 2*sinx)
  • -(x/4cosx)+(4/x^2sinx)
  • -(x/4cosx)+(4/x2sinx)
  • -x/4cosx+4/x2sinx
  • -x/4cosx+4/x^2sinx
  • -(x divide by 4*cosx)+(4 divide by x^2*sinx)

  • Similar expressions

  • -(x/4*cosx)-(4/x^2*sinx)
  • (x/4*cosx)+(4/x^2*sinx)
The derivative of the function/ -(x/4*cosx)+(4/x^2*sinx)

Derivative of -(x/4*cosx)+(4/x^2*sinx)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  x          4        
- -*cos(x) + --*sin(x)
  4           2       
             x
$$- \frac{x}{4} \cos{\left(x \right)} + \frac{4}{x^{2}} \sin{\left(x \right)}$$ 
-x/4*cos(x) + (4/x^2)*sin(x)
Detail solution

  1. Differentiate term by term:

    1. 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. Apply the product rule:

          ; to find :

          1. Apply the power rule: goes to

          ; to find :

          1. The derivative of cosine is negative sine:

          The result is:

        So, the result is:

      So, the result is:

    2. Apply the quotient rule, which is:

      and .

      To find :

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

        1. The derivative of sine is cosine:

        So, the result is:

      To find :

      1. Apply the power rule: goes to

      Now plug in to the quotient rule:

    The result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  cos(x)   8*sin(x)   4*cos(x)   x*sin(x)
- ------ - -------- + -------- + --------
    4          3          2         4    
              x          x
$$\frac{x \sin{\left(x \right)}}{4} - \frac{\cos{\left(x \right)}}{4} + \frac{4 \cos{\left(x \right)}}{x^{2}} - \frac{8 \sin{\left(x \right)}}{x^{3}}$$
Simplify
The second derivative [src] 
sin(x)   16*cos(x)   4*sin(x)   24*sin(x)   x*cos(x)
------ - --------- - -------- + --------- + --------
  2           3          2           4         4    
             x          x           x
$$\frac{x \cos{\left(x \right)}}{4} + \frac{\sin{\left(x \right)}}{2} - \frac{4 \sin{\left(x \right)}}{x^{2}} - \frac{16 \cos{\left(x \right)}}{x^{3}} + \frac{24 \sin{\left(x \right)}}{x^{4}}$$
Simplify
The third derivative [src] 
3*cos(x)   96*sin(x)   4*cos(x)   24*sin(x)   72*cos(x)   x*sin(x)
-------- - --------- - -------- + --------- + --------- - --------
   4            5          2           3           4         4    
               x          x           x           x
$$- \frac{x \sin{\left(x \right)}}{4} + \frac{3 \cos{\left(x \right)}}{4} - \frac{4 \cos{\left(x \right)}}{x^{2}} + \frac{24 \sin{\left(x \right)}}{x^{3}} + \frac{72 \cos{\left(x \right)}}{x^{4}} - \frac{96 \sin{\left(x \right)}}{x^{5}}$$
Simplify
    © Mister Exam – Calculator