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Derivative of:
Derivative of x/6
Derivative of x*3
Derivative of log(x^4+x)
Derivative of ln(4x)
Identical expressions
сos^ two (x- seven)
сos squared (x minus 7)
сos to the power of two (x minus seven)
сos2(x-7)
сos2x-7
сos²(x-7)
сos to the power of 2(x-7)
сos^2x-7
Similar expressions
сos^2(x+7)

The derivative of the function/ сos^2(x-7)

Derivative of сos^2(x-7)

The solution

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   2       
cos (x - 7)

$$\cos^{2}{\left(x - 7 \right)}$$

cos(x - 7)^2

Detail solution

Let $u = \cos{\left(x - 7 \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \cos{\left(x - 7 \right)}$ :
1. Let $u = x - 7$ .
2. The derivative of cosine is negative sine:
  
  $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x - 7\right)$ :
  1. Differentiate $x - 7$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $-7$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $- \sin{\left(x - 7 \right)}$
The result of the chain rule is:

$- 2 \sin{\left(x - 7 \right)} \cos{\left(x - 7 \right)}$
Now simplify:

$- \sin{\left(2 x - 14 \right)}$

The answer is:

$- \sin{\left(2 x - 14 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*cos(x - 7)*sin(x - 7)

$$- 2 \sin{\left(x - 7 \right)} \cos{\left(x - 7 \right)}$$

Simplify

The second derivative [src]

  /   2              2        \
2*\sin (-7 + x) - cos (-7 + x)/

$$2 \left(\sin^{2}{\left(x - 7 \right)} - \cos^{2}{\left(x - 7 \right)}\right)$$

Simplify

The third derivative [src]

8*cos(-7 + x)*sin(-7 + x)

$$8 \sin{\left(x - 7 \right)} \cos{\left(x - 7 \right)}$$

Simplify

The graph

Derivative of сos^2(x-7)