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The derivative of the function/ y=sin^2x-sinx

Derivative of y=sin^2x-sinx

The solution

You have entered [src]

   2            
sin (x) - sin(x)

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

sin(x)^2 - sin(x)

Detail solution

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

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

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

Simplify

The second derivative [src]

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

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

Simplify

The graph

Derivative of y=sin^2x-sinx