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2*sin(x)+(3/2)*cos(x)
The derivative of the function/ 2*sin(x)+(3/2)*cos(x)

Derivative of 2*sin(x)+(3/2)*cos(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
           3*cos(x)
2*sin(x) + --------
              2
$$2 \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{2}$$ 
2*sin(x) + 3*cos(x)/2
Detail solution

  1. Differentiate term by term:

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of sine is cosine:

      So, the result is:

    2. The derivative of a constant times a function is the constant times the derivative of the function.

      1. The derivative of cosine is negative sine:

      So, the result is:

    The result is:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
           3*sin(x)
2*cos(x) - --------
              2
$$- \frac{3 \sin{\left(x \right)}}{2} + 2 \cos{\left(x \right)}$$
Simplify
The second derivative [src] 
 /           3*cos(x)\
-|2*sin(x) + --------|
 \              2    /
$$- (2 \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{2})$$
Simplify
The third derivative [src] 
            3*sin(x)
-2*cos(x) + --------
               2
$$\frac{3 \sin{\left(x \right)}}{2} - 2 \cos{\left(x \right)}$$
Simplify
The graph
Derivative of 2*sin(x)+(3/2)*cos(x)
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