Mister Exam

Other calculators

  • How to use it?

  • Derivative of:
  • Derivative of x^3/cosx Derivative of x^3/cosx
  • Derivative of (x-5)^2*e^x-7 Derivative of (x-5)^2*e^x-7
  • Derivative of x/(1+e^x) Derivative of x/(1+e^x)
  • Derivative of e^(3/x) Derivative of e^(3/x)

  • Identical expressions

  • sqrt(three)*sin(x)+(x^ two /pi)+(x)sinpi/ six
  • square root of (3) multiply by sinus of (x) plus (x squared divide by Pi ) plus (x) sinus of Pi divide by 6
  • square root of (three) multiply by sinus of (x) plus (x to the power of two divide by Pi ) plus (x) sinus of Pi divide by six
  • √(3)*sin(x)+(x^2/pi)+(x)sinpi/6
  • sqrt(3)*sin(x)+(x2/pi)+(x)sinpi/6
  • sqrt3*sinx+x2/pi+xsinpi/6
  • sqrt(3)*sin(x)+(x²/pi)+(x)sinpi/6
  • sqrt(3)*sin(x)+(x to the power of 2/pi)+(x)sinpi/6
  • sqrt(3)sin(x)+(x^2/pi)+(x)sinpi/6
  • sqrt(3)sin(x)+(x2/pi)+(x)sinpi/6
  • sqrt3sinx+x2/pi+xsinpi/6
  • sqrt3sinx+x^2/pi+xsinpi/6
  • sqrt(3)*sin(x)+(x^2 divide by pi)+(x)sinpi divide by 6

  • Similar expressions

  • sqrt(3)*sin(x)+(x^2/pi)-(x)sinpi/6
  • sqrt(3)*sin(x)-(x^2/pi)+(x)sinpi/6
  • sqrt(3)*sinx+(x^2/pi)+(x)sinpi/6
The derivative of the function/ sqrt(3)*sin(x)+(x^2/pi)+(x)sinpi/6

Derivative of sqrt(3)*sin(x)+(x^2/pi)+(x)sinpi/6

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
                2            
  ___          x    x*sin(pi)
\/ 3 *sin(x) + -- + ---------
               pi       6
$$\frac{x \sin{\left(\pi \right)}}{6} + \left(\frac{x^{2}}{\pi} + \sqrt{3} \sin{\left(x \right)}\right)$$ 
sqrt(3)*sin(x) + x^2/pi + (x*sin(pi))/6
Detail solution

  1. Differentiate term by term:

    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 sine is cosine:

        So, the result is:

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

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    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. Apply the power rule: goes to

        So, the result is:

      So, the result is:

    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] 
sin(pi)     ___          2*x
------- + \/ 3 *cos(x) + ---
   6                      pi
$$\frac{2 x}{\pi} + \sqrt{3} \cos{\left(x \right)} + \frac{\sin{\left(\pi \right)}}{6}$$
Simplify
The second derivative [src] 
2      ___       
-- - \/ 3 *sin(x)
pi
$$- \sqrt{3} \sin{\left(x \right)} + \frac{2}{\pi}$$
Simplify
The third derivative [src] 
   ___       
-\/ 3 *cos(x)
$$- \sqrt{3} \cos{\left(x \right)}$$
Simplify
    © Mister Exam – Calculator