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Derivative of:
Derivative of x^-(4/5)
Derivative of sec2x
Derivative of x^2*tgx
Derivative of sin(5)^(3)*x
Graphing y =:
sin2x-cos^2x
Identical expressions
y=sin2x-cos^2x
y equally sinus of 2x minus co sinus of e of squared x
y=sin2x-cos2x
y=sin2x-cos²x
y=sin2x-cos to the power of 2x
Similar expressions
y=sin2x+cos^2x

The derivative of the function/ y=sin2x-cos^2x

Derivative of y=sin2x-cos^2x

The solution

You have entered [src]

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

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

d /              2   \
--\sin(2*x) - cos (x)/
dx

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

Transform

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2*cos(2*x) + 2*cos(x)*sin(x)

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

-8*(cos(x)*sin(x) + cos(2*x))

$$- 8 \left(\sin{\left(x \right)} \cos{\left(x \right)} + \cos{\left(2 x \right)}\right)$$

Simplify

The graph

Derivative of y=sin2x-cos^2x