Mister Exam

Derivative of y=e^(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)
$$e^{2 x} + \sin{\left(3 x \right)}$$
d / 2*x           \
--\e    + sin(3*x)/
dx                 
$$\frac{d}{d x} \left(e^{2 x} + \sin{\left(3 x \right)}\right)$$
Detail solution
  1. Differentiate term by term:

    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:

    4. Let .

    5. The derivative of sine is cosine:

    6. 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:


The answer is:

The graph
The first derivative [src]
   2*x             
2*e    + 3*cos(3*x)
$$2 e^{2 x} + 3 \cos{\left(3 x \right)}$$
The second derivative [src]
                 2*x
-9*sin(3*x) + 4*e   
$$4 e^{2 x} - 9 \sin{\left(3 x \right)}$$
The third derivative [src]
                  2*x
-27*cos(3*x) + 8*e   
$$8 e^{2 x} - 27 \cos{\left(3 x \right)}$$
The graph
Derivative of y=e^(2x)+sin(3x)