Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of sinx^2
Derivative of acos(2x)
Derivative of x*cos(x+3)+7
Derivative of log0,5(x)
Identical expressions
cosx^ four -sinx^ four
co sinus of e of x to the power of 4 minus sinus of x to the power of 4
co sinus of e of x to the power of four minus sinus of x to the power of four
cosx4-sinx4
cosx⁴-sinx⁴
Similar expressions
cosx^4+sinx^4

The derivative of the function/ cosx^4-sinx^4

Derivative of cosx^4-sinx^4

The solution

You have entered [src]

   4         4   
cos (x) - sin (x)

$$- \sin^{4}{\left(x \right)} + \cos^{4}{\left(x \right)}$$

d /   4         4   \
--\cos (x) - sin (x)/
dx

$$\frac{d}{d x} \left(- \sin^{4}{\left(x \right)} + \cos^{4}{\left(x \right)}\right)$$

Transform

Detail solution

Differentiate $- \sin^{4}{\left(x \right)} + \cos^{4}{\left(x \right)}$ term by term:
1. Let $u = \cos{\left(x \right)}$ .
2. Apply the power rule: $u^{4}$ goes to $4 u^{3}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(x \right)}$ :
  1. The derivative of cosine is negative sine:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  The result of the chain rule is:
  
  $- 4 \sin{\left(x \right)} \cos^{3}{\left(x \right)}$
4. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \sin{\left(x \right)}$ .
  2. Apply the power rule: $u^{4}$ goes to $4 u^{3}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sin{\left(x \right)}$ :
    1. The derivative of sine is cosine:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
    The result of the chain rule is:
    
    $4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}$
  So, the result is: $- 4 \sin^{3}{\left(x \right)} \cos{\left(x \right)}$
The result is: $- 4 \sin^{3}{\left(x \right)} \cos{\left(x \right)} - 4 \sin{\left(x \right)} \cos^{3}{\left(x \right)}$
Now simplify:

$- 2 \sin{\left(2 x \right)}$

The answer is:

$- 2 \sin{\left(2 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       3                  3          
- 4*cos (x)*sin(x) - 4*sin (x)*cos(x)

$$- 4 \sin^{3}{\left(x \right)} \cos{\left(x \right)} - 4 \sin{\left(x \right)} \cos^{3}{\left(x \right)}$$

Simplify

The second derivative [src]

  /   4         4   \
4*\sin (x) - cos (x)/

$$4 \left(\sin^{4}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)$$

Simplify

The third derivative [src]

   /   2         2   \              
16*\cos (x) + sin (x)/*cos(x)*sin(x)

$$16 \left(\sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The graph

Derivative of cosx^4-sinx^4