Mister Exam

Other calculators

8sinx-30/п×x+5
The derivative of the function/ 8sinx-30/п×x+5

You entered:

8sinx-30/п×x+5

What you mean?

(8*sin(x) - 1*30)/(pi*x + 5)
 
(8*sin(x) - 1*30)/((pi*x)) + 5
 
(8*sin(x) - 1*30)*x/pi + 5
 
8*(sin(x) - 1*30)/(pi*x + 5)
 
8*(sin(x) - 1*30)/((pi*x)) + 5
 
8*(sin(x) - 1*30)*x/pi + 5
 
8*sin(x) - 30*x/pi + 5

Derivative of 8sinx-30/п×x+5

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
           30*x    
8*sin(x) - ---- + 5
            pi
$$- \frac{30 x}{\pi} + 8 \sin{\left(x \right)} + 5$$ 
d /           30*x    \
--|8*sin(x) - ---- + 5|
dx\            pi     /
$$\frac{d}{d x} \left(- \frac{30 x}{\pi} + 8 \sin{\left(x \right)} + 5\right)$$
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 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. 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:

    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*cos(x)
  pi
$$8 \cos{\left(x \right)} - \frac{30}{\pi}$$
Simplify
The second derivative [src] 
-8*sin(x)
$$- 8 \sin{\left(x \right)}$$
Simplify
The third derivative [src] 
-8*cos(x)
$$- 8 \cos{\left(x \right)}$$
Simplify
The graph
Derivative of 8sinx-30/п×x+5
    © Mister Exam – Calculator