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The derivative of the function/ sin(nx)

Derivative of sin(nx)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
sin(n*x)
sin⁡(nx)\sin{\left(n x \right)} 
sin(n*x)
Detail solution

  1. Let u=nxu = n x.

  2. The derivative of sine is cosine:

    ddusin⁡(u)=cos⁡(u)\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}

  3. Then, apply the chain rule. Multiply by ∂∂xnx\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: xx goes to 11

      So, the result is: nn

    The result of the chain rule is:

    ncos⁡(nx)n \cos{\left(n x \right)}

The answer is:

ncos⁡(nx)n \cos{\left(n x \right)}

The first derivative [src] 
n*cos(n*x)
ncos⁡(nx)n \cos{\left(n x \right)}
Simplify
The second derivative [src] 
  2         
-n *sin(n*x)
−n2sin⁡(nx)- n^{2} \sin{\left(n x \right)}
Simplify
The third derivative [src] 
  3         
-n *cos(n*x)
−n3cos⁡(nx)- n^{3} \cos{\left(n x \right)}
Simplify
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