Mister Exam

Derivative of sin²x-cos²x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2         2   
sin (x) - cos (x)
$$\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}$$
d /   2         2   \
--\sin (x) - cos (x)/
dx                   
$$\frac{d}{d x} \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)$$
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. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Let .

      2. Apply the power rule: goes to

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

        1. The derivative of cosine is negative sine:

        The result of the chain rule is:

      So, the result is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
4*cos(x)*sin(x)
$$4 \sin{\left(x \right)} \cos{\left(x \right)}$$
The second derivative [src]
  /   2         2   \
4*\cos (x) - sin (x)/
$$4 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)$$
The third derivative [src]
-16*cos(x)*sin(x)
$$- 16 \sin{\left(x \right)} \cos{\left(x \right)}$$
The graph
Derivative of sin²x-cos²x