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Derivative of 1/2cosx²-sin²x

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   2             
cos (x)      2   
------- - sin (x)
   2             
$$- \sin^{2}{\left(x \right)} + \frac{\cos^{2}{\left(x \right)}}{2}$$
cos(x)^2/2 - sin(x)^2
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. 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:

    2. 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 sine is cosine:

        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]
-3*cos(x)*sin(x)
$$- 3 \sin{\left(x \right)} \cos{\left(x \right)}$$
The second derivative [src]
  /   2         2   \
3*\sin (x) - cos (x)/
$$3 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)$$
The third derivative [src]
12*cos(x)*sin(x)
$$12 \sin{\left(x \right)} \cos{\left(x \right)}$$