Mister Exam

Derivative of exp(2x)*sin(3x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2*x         
e   *sin(3*x)
$$e^{2 x} \sin{\left(3 x \right)}$$
exp(2*x)*sin(3*x)
Detail solution
  1. Apply the product rule:

    ; to find :

    1. Let .

    2. The derivative of is itself.

    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:

    ; to find :

    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:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   2*x                        2*x
2*e   *sin(3*x) + 3*cos(3*x)*e   
$$2 e^{2 x} \sin{\left(3 x \right)} + 3 e^{2 x} \cos{\left(3 x \right)}$$
The second derivative [src]
                             2*x
(-5*sin(3*x) + 12*cos(3*x))*e   
$$\left(- 5 \sin{\left(3 x \right)} + 12 \cos{\left(3 x \right)}\right) e^{2 x}$$
The third derivative [src]
                             2*x
(-46*sin(3*x) + 9*cos(3*x))*e   
$$\left(- 46 \sin{\left(3 x \right)} + 9 \cos{\left(3 x \right)}\right) e^{2 x}$$