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Derivative of:
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Derivative of sin(x)+3
Identical expressions
eighteen *sin^ two (x)- two
18 multiply by sinus of squared (x) minus 2
eighteen multiply by sinus of to the power of two (x) minus two
18*sin2(x)-2
18*sin2x-2
18*sin²(x)-2
18*sin to the power of 2(x)-2
18sin^2(x)-2
18sin2(x)-2
18sin2x-2
18sin^2x-2
Similar expressions
18*sin^2(x)+2

The derivative of the function/ 18*sin^2(x)-2

Derivative of 18*sin^2(x)-2

The solution

You have entered [src]

      2       
18*sin (x) - 2

$$18 \sin^{2}{\left(x \right)} - 2$$

18*sin(x)^2 - 2

Detail solution

Differentiate $18 \sin^{2}{\left(x \right)} - 2$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  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:
    
    $2 \sin{\left(x \right)} \cos{\left(x \right)}$
  So, the result is: $36 \sin{\left(x \right)} \cos{\left(x \right)}$
2. The derivative of the constant $-2$ is zero.
The result is: $36 \sin{\left(x \right)} \cos{\left(x \right)}$
Now simplify:

$18 \sin{\left(2 x \right)}$

The answer is:

$18 \sin{\left(2 x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

36*cos(x)*sin(x)

$$36 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The second derivative [src]

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

$$36 \left(- \sin^{2}{\left(x \right)} + \cos^{2}{\left(x \right)}\right)$$

Simplify

The third derivative [src]

-144*cos(x)*sin(x)

$$- 144 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify