Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (x^2-2*x+8)^(1/5)
Derivative of (x-2)^(1/2)
Derivative of x*10^x
Derivative of 3*sin(5*x)
Identical expressions
(-cos(10x))/ twenty +(cos(6x))/ twelve
( minus co sinus of e of (10x)) divide by 20 plus ( co sinus of e of (6x)) divide by 12
( minus co sinus of e of (10x)) divide by twenty plus ( co sinus of e of (6x)) divide by twelve
-cos10x/20+cos6x/12
(-cos(10x)) divide by 20+(cos(6x)) divide by 12
Similar expressions
(cos(10x))/20+(cos(6x))/12
(-cos(10x))/20-(cos(6x))/12

The derivative of the function/ (-cos(10x))/20+(cos(6x))/12

Derivative of (-cos(10x))/20+(cos(6x))/12

The solution

You have entered [src]

-cos(10*x)    cos(6*x)
----------- + --------
     20          12

$$\frac{\cos{\left(6 x \right)}}{12} + \frac{\left(-1\right) \cos{\left(10 x \right)}}{20}$$

(-cos(10*x))/20 + cos(6*x)/12

Detail solution

Differentiate $\frac{\cos{\left(6 x \right)}}{12} + \frac{\left(-1\right) \cos{\left(10 x \right)}}{20}$ 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. Let $u = 10 x$ .
    2. The derivative of cosine is negative sine:
      
      $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 10 x$ :
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $10$
      The result of the chain rule is:
      
      $- 10 \sin{\left(10 x \right)}$
    So, the result is: $10 \sin{\left(10 x \right)}$
  So, the result is: $\frac{\sin{\left(10 x \right)}}{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 6 x$ .
  2. The derivative of cosine is negative sine:
    
    $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 6 x$ :
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x$ goes to $1$
      So, the result is: $6$
    The result of the chain rule is:
    
    $- 6 \sin{\left(6 x \right)}$
  So, the result is: $- \frac{\sin{\left(6 x \right)}}{2}$
The result is: $- \frac{\sin{\left(6 x \right)}}{2} + \frac{\sin{\left(10 x \right)}}{2}$

The answer is:

$- \frac{\sin{\left(6 x \right)}}{2} + \frac{\sin{\left(10 x \right)}}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

sin(10*x)   sin(6*x)
--------- - --------
    2          2

$$- \frac{\sin{\left(6 x \right)}}{2} + \frac{\sin{\left(10 x \right)}}{2}$$

Simplify

The second derivative [src]

-3*cos(6*x) + 5*cos(10*x)

$$- 3 \cos{\left(6 x \right)} + 5 \cos{\left(10 x \right)}$$

Simplify

The third derivative [src]

2*(-25*sin(10*x) + 9*sin(6*x))

$$2 \left(9 \sin{\left(6 x \right)} - 25 \sin{\left(10 x \right)}\right)$$

Simplify

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of (-cos(10x))/20+(cos(6x))/12

The graph:

Piecewise:

The solution