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cos^2x
The derivative of the function/ cos^2x

Derivative of cos^2x

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

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The solution

You have entered [src] 
   2   
cos (x)
cos⁡2(x)\cos^{2}{\left(x \right)} 
cos(x)^2
Detail solution

  1. Let u=cos⁡(x)u = \cos{\left(x \right)}.

  2. Apply the power rule: u2u^{2} goes to 2u2 u

  3. Then, apply the chain rule. Multiply by ddxcos⁡(x)\frac{d}{d x} \cos{\left(x \right)}:

    1. The derivative of cosine is negative sine:

      ddxcos⁡(x)=−sin⁡(x)\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}

    The result of the chain rule is:

    −2sin⁡(x)cos⁡(x)- 2 \sin{\left(x \right)} \cos{\left(x \right)}

  4. Now simplify:

    −sin⁡(2x)- \sin{\left(2 x \right)}

The answer is:

−sin⁡(2x)- \sin{\left(2 x \right)}

The graph
02468-8-6-4-2-10102-2
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
-2*cos(x)*sin(x)
−2sin⁡(x)cos⁡(x)- 2 \sin{\left(x \right)} \cos{\left(x \right)}
Simplify
The second derivative [src] 
  /   2         2   \
2*\sin (x) - cos (x)/
2(sin⁡2(x)−cos⁡2(x))2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)
Simplify
The third derivative [src] 
8*cos(x)*sin(x)
8sin⁡(x)cos⁡(x)8 \sin{\left(x \right)} \cos{\left(x \right)}
Simplify
The graph
Derivative of cos^2x
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