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Derivative of:
Derivative of x^6
Derivative of sqrt(1-3x^2)
Derivative of cost^2
Derivative of x^2cosx
Integral of d{x}:
cost^2
Identical expressions
cost^ two
co sinus of e of t squared
co sinus of e of t to the power of two
cost2
cost²
cost to the power of 2
Similar expressions
(cos(t))^2

The derivative of the function/ cost^2

Derivative of cost^2

The solution

You have entered [src]

   2   
cos (t)

$$\cos^{2}{\left(t \right)}$$

d /   2   \
--\cos (t)/
dt

$$\frac{d}{d t} \cos^{2}{\left(t \right)}$$

Transform

Detail solution

Let $u = \cos{\left(t \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d t} \cos{\left(t \right)}$ :
1. The derivative of cosine is negative sine:
  
  $\frac{d}{d t} \cos{\left(t \right)} = - \sin{\left(t \right)}$
The result of the chain rule is:

$- 2 \sin{\left(t \right)} \cos{\left(t \right)}$
Now simplify:

$- \sin{\left(2 t \right)}$

The answer is:

$- \sin{\left(2 t \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*cos(t)*sin(t)

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

Simplify

The second derivative [src]

  /   2         2   \
2*\sin (t) - cos (t)/

$$2 \left(\sin^{2}{\left(t \right)} - \cos^{2}{\left(t \right)}\right)$$

Simplify

The third derivative [src]

8*cos(t)*sin(t)

$$8 \sin{\left(t \right)} \cos{\left(t \right)}$$

Simplify

The graph

Derivative of cost^2