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Derivative of:
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Derivative of 9x-9ln(x+11)+7
Identical expressions
sin(n^ two *x)/ two
sinus of (n squared multiply by x) divide by 2
sinus of (n to the power of two multiply by x) divide by two
sin(n2*x)/2
sinn2*x/2
sin(n²*x)/2
sin(n to the power of 2*x)/2
sin(n^2x)/2
sin(n2x)/2
sinn2x/2
sinn^2x/2
sin(n^2*x) divide by 2

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

Derivative of sin(n^2*x)/2

The solution

You have entered [src]

   / 2  \
sin\n *x/
---------
    2

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

sin(n^2*x)/2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = n^{2} x$ .
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 $\frac{\partial}{\partial x} n^{2} x$ :
  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: $n^{2}$
  The result of the chain rule is:
  
  $n^{2} \cos{\left(n^{2} x \right)}$
So, the result is: $\frac{n^{2} \cos{\left(n^{2} x \right)}}{2}$
Now simplify:

$\frac{n^{2} \cos{\left(n^{2} x \right)}}{2}$

The answer is:

$\frac{n^{2} \cos{\left(n^{2} x \right)}}{2}$

The first derivative [src]

 2    / 2  \
n *cos\n *x/
------------
     2

$$\frac{n^{2} \cos{\left(n^{2} x \right)}}{2}$$

Simplify

The second derivative [src]

  4    /   2\ 
-n *sin\x*n / 
--------------
      2

$$- \frac{n^{4} \sin{\left(n^{2} x \right)}}{2}$$

Simplify

The third derivative [src]

  6    /   2\ 
-n *cos\x*n / 
--------------
      2

$$- \frac{n^{6} \cos{\left(n^{2} x \right)}}{2}$$

Simplify