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

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Derivative of:
Derivative of x^(4/5)
Derivative of x^3+2
Derivative of x^2-7*x
Derivative of ln(x)^2
Identical expressions
(exp^- two)*sin(4x)
( exponent of to the power of minus 2) multiply by sinus of (4x)
( exponent of to the power of minus two) multiply by sinus of (4x)
(exp-2)*sin(4x)
exp-2*sin4x
(exp^-2)sin(4x)
(exp-2)sin(4x)
exp-2sin4x
exp^-2sin4x
Similar expressions
(exp^+2)*sin(4x)

The derivative of the function/ (exp^-2)*sin(4x)

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

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    /

$$\frac{d}{d x} \frac{\sin{\left(4 x \right)}}{e^{2}}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 4 x$ .
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 $\frac{d}{d x} 4 x$ :
  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: $4$
  The result of the chain rule is:
  
  $4 \cos{\left(4 x \right)}$
So, the result is: $\frac{4 \cos{\left(4 x \right)}}{e^{2}}$

The answer is:

$\frac{4 \cos{\left(4 x \right)}}{e^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            -2
4*cos(4*x)*e

$$\frac{4 \cos{\left(4 x \right)}}{e^{2}}$$

Simplify

The second derivative [src]

     -2         
-16*e  *sin(4*x)

$$- \frac{16 \sin{\left(4 x \right)}}{e^{2}}$$

Simplify

The third derivative [src]

              -2
-64*cos(4*x)*e

$$- \frac{64 \cos{\left(4 x \right)}}{e^{2}}$$

Simplify

The graph

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