Mister Exam

Other calculators


(exp^-2)*sin(4x)

Derivative of (exp^-2)*sin(4x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(4*x)
--------
    2   
   e    
$$\frac{\sin{\left(4 x \right)}}{e^{2}}$$
d /sin(4*x)\
--|--------|
dx|    2   |
  \   e    /
$$\frac{d}{d x} \frac{\sin{\left(4 x \right)}}{e^{2}}$$
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Let .

    2. The derivative of sine is cosine:

    3. Then, apply the chain rule. Multiply by :

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result of the chain rule is:

    So, the result is:


The answer is:

The graph
The first derivative [src]
            -2
4*cos(4*x)*e  
$$\frac{4 \cos{\left(4 x \right)}}{e^{2}}$$
The second derivative [src]
     -2         
-16*e  *sin(4*x)
$$- \frac{16 \sin{\left(4 x \right)}}{e^{2}}$$
The third derivative [src]
              -2
-64*cos(4*x)*e  
$$- \frac{64 \cos{\left(4 x \right)}}{e^{2}}$$
The graph
Derivative of (exp^-2)*sin(4x)