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Derivative of:
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Identical expressions
cos^2x+ one +sinx
co sinus of e of squared x plus 1 plus sinus of x
co sinus of e of squared x plus one plus sinus of x
cos2x+1+sinx
cos²x+1+sinx
cos to the power of 2x+1+sinx
Similar expressions
cos^2x-1+sinx
cos^2x+1-sinx

The derivative of the function/ cos^2x+1+sinx

Derivative of cos^2x+1+sinx

The solution

You have entered [src]

   2                
cos (x) + 1 + sin(x)

$$\left(\cos^{2}{\left(x \right)} + 1\right) + \sin{\left(x \right)}$$

cos(x)^2 + 1 + sin(x)

Detail solution

Differentiate $\left(\cos^{2}{\left(x \right)} + 1\right) + \sin{\left(x \right)}$ term by term:
1. Differentiate $\cos^{2}{\left(x \right)} + 1$ term by term:
  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:
    
    $- 2 \sin{\left(x \right)} \cos{\left(x \right)}$
  4. The derivative of the constant $1$ is zero.
  The result is: $- 2 \sin{\left(x \right)} \cos{\left(x \right)}$
2. The derivative of sine is cosine:
  
  $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
The result is: $- 2 \sin{\left(x \right)} \cos{\left(x \right)} + \cos{\left(x \right)}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

(-1 + 8*sin(x))*cos(x)

$$\left(8 \sin{\left(x \right)} - 1\right) \cos{\left(x \right)}$$

Simplify