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Identical expressions
cos^2x+sinx− one
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cos2x+sinx−1
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Similar expressions
cos^2x-sinx−1

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

Derivative of cos^2x+sinx−1

The solution

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

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

d /   2                \
--\cos (x) + sin(x) - 1/
dx

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

Transform

Detail solution

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

The graph

Derivative of cos^2x+sinx−1