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e^(2*x)*sin(x)

Derivative of e^(2*x)*sin(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2*x       
e   *sin(x)
$$e^{2 x} \sin{\left(x \right)}$$
d / 2*x       \
--\e   *sin(x)/
dx             
$$\frac{d}{d x} e^{2 x} \sin{\left(x \right)}$$
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. The derivative of sine is cosine:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
        2*x      2*x       
cos(x)*e    + 2*e   *sin(x)
$$2 e^{2 x} \sin{\left(x \right)} + e^{2 x} \cos{\left(x \right)}$$
The second derivative [src]
                       2*x
(3*sin(x) + 4*cos(x))*e   
$$\left(3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}\right) e^{2 x}$$
The third derivative [src]
                        2*x
(2*sin(x) + 11*cos(x))*e   
$$\left(2 \sin{\left(x \right)} + 11 \cos{\left(x \right)}\right) e^{2 x}$$
The graph
Derivative of e^(2*x)*sin(x)