Mister Exam

Derivative of sin^4x+cos^4x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   4         4   
sin (x) + cos (x)
$$\sin^{4}{\left(x \right)} + \cos^{4}{\left(x \right)}$$
d /   4         4   \
--\sin (x) + cos (x)/
dx                   
$$\frac{d}{d x} \left(\sin^{4}{\left(x \right)} + \cos^{4}{\left(x \right)}\right)$$
Detail solution
  1. Differentiate term by term:

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of sine is cosine:

      The result of the chain rule is:

    4. Let .

    5. Apply the power rule: goes to

    6. Then, apply the chain rule. Multiply by :

      1. The derivative of cosine is negative sine:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
       3                  3          
- 4*cos (x)*sin(x) + 4*sin (x)*cos(x)
$$4 \sin^{3}{\left(x \right)} \cos{\left(x \right)} - 4 \sin{\left(x \right)} \cos^{3}{\left(x \right)}$$
The second derivative [src]
  /     4         4           2       2   \
4*\- cos (x) - sin (x) + 6*cos (x)*sin (x)/
$$4 \left(- \sin^{4}{\left(x \right)} + 6 \sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)} - \cos^{4}{\left(x \right)}\right)$$
The third derivative [src]
   /   2         2   \              
64*\cos (x) - sin (x)/*cos(x)*sin(x)
$$64 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)} \cos{\left(x \right)}$$
The graph
Derivative of sin^4x+cos^4x