Mister Exam

Other calculators

8*cos(x)+(30/pi)*x+19
The derivative of the function/ 8*cos(x)+(30/pi)*x+19

Derivative of 8*cos(x)+(30/pi)*x+19

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
           30*x     
8*cos(x) + ---- + 19
            pi
$$\frac{30 x}{\pi} + 8 \cos{\left(x \right)} + 19$$ 
d /           30*x     \
--|8*cos(x) + ---- + 19|
dx\            pi      /
$$\frac{d}{d x} \left(\frac{30 x}{\pi} + 8 \cos{\left(x \right)} + 19\right)$$
Transform
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 cosine is negative sine:

      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:

    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] 
            30
-8*sin(x) + --
            pi
$$- 8 \sin{\left(x \right)} + \frac{30}{\pi}$$
Simplify
The second derivative [src] 
-8*cos(x)
$$- 8 \cos{\left(x \right)}$$
Simplify
The third derivative [src] 
8*sin(x)
$$8 \sin{\left(x \right)}$$
Simplify
The graph
Derivative of 8*cos(x)+(30/pi)*x+19
    © Mister Exam – Calculator