Derivative of sin(nx)

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sin(n*x)

$$\sin{\left(n x \right)}$$

sin(n*x)

Detail solution

Let $u = n x$ .
The derivative of sine is cosine:

$\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
Then, apply the chain rule. Multiply by $\frac{\partial}{\partial x} n x$ :
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: $n$
The result of the chain rule is:

$n \cos{\left(n x \right)}$

The answer is:

$n \cos{\left(n x \right)}$

The first derivative [src]

n*cos(n*x)

$$n \cos{\left(n x \right)}$$

Simplify

The second derivative [src]

  2         
-n *sin(n*x)

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

Simplify

The third derivative [src]

  3         
-n *cos(n*x)

$$- n^{3} \cos{\left(n x \right)}$$

Simplify