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cost^2
The derivative of the function/ cost^2

Derivative of cost^2

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   2   
cos (t)
cos⁡2(t)\cos^{2}{\left(t \right)} 
d /   2   \
--\cos (t)/
dt
ddtcos⁡2(t)\frac{d}{d t} \cos^{2}{\left(t \right)}
Transform
Detail solution

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

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

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

    1. The derivative of cosine is negative sine:

      ddtcos⁡(t)=−sin⁡(t)\frac{d}{d t} \cos{\left(t \right)} = - \sin{\left(t \right)}

    The result of the chain rule is:

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

  4. Now simplify:

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

The answer is:

−sin⁡(2t)- \sin{\left(2 t \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(t)*sin(t)
−2sin⁡(t)cos⁡(t)- 2 \sin{\left(t \right)} \cos{\left(t \right)}
Simplify
The second derivative [src] 
  /   2         2   \
2*\sin (t) - cos (t)/
2(sin⁡2(t)−cos⁡2(t))2 \left(\sin^{2}{\left(t \right)} - \cos^{2}{\left(t \right)}\right)
Simplify
The third derivative [src] 
8*cos(t)*sin(t)
8sin⁡(t)cos⁡(t)8 \sin{\left(t \right)} \cos{\left(t \right)}
Simplify
The graph
Derivative of cost^2
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