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y(x)=3e^-3cos(3x)
The derivative of the function/ y(x)=3e^-3cos(3x)

You entered:

y(x)=3e^-3cos(3x)

What you mean?

3*cos(3*x)/e^3
 
3*3*x/e^(3*cos(x))
 
3*3*x/e^(3*cos(x))

Derivative of y(x)=3e^-3cos(3x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
3*cos(3*x)
----------
     3    
    e
$$\frac{3 \cos{\left(3 x \right)}}{e^{3}}$$ 
d /3*cos(3*x)\
--|----------|
dx|     3    |
  \    e     /
$$\frac{d}{d x} \frac{3 \cos{\left(3 x \right)}}{e^{3}}$$
Transform
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 cosine is negative sine:

    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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    -3         
-9*e  *sin(3*x)
$$- \frac{9 \sin{\left(3 x \right)}}{e^{3}}$$
Simplify
The second derivative [src] 
              -3
-27*cos(3*x)*e
$$- \frac{27 \cos{\left(3 x \right)}}{e^{3}}$$
Simplify
The third derivative [src] 
    -3         
81*e  *sin(3*x)
$$\frac{81 \sin{\left(3 x \right)}}{e^{3}}$$
Simplify
The graph
Derivative of y(x)=3e^-3cos(3x)
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