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(2*sin(x)+1,5*cos(x))

Derivative of (2*sin(x)+1,5*cos(x))

Function f() - derivative -N order at the point
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The graph:

from to

Piecewise:

The solution

You have entered [src]
           3*cos(x)
2*sin(x) + --------
              2    
$$2 \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{2}$$
d /           3*cos(x)\
--|2*sin(x) + --------|
dx\              2    /
$$\frac{d}{d x} \left(2 \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{2}\right)$$
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
The first derivative [src]
           3*sin(x)
2*cos(x) - --------
              2    
$$- \frac{3 \sin{\left(x \right)}}{2} + 2 \cos{\left(x \right)}$$
The second derivative [src]
 /           3*cos(x)\
-|2*sin(x) + --------|
 \              2    /
$$- (2 \sin{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{2})$$
The third derivative [src]
            3*sin(x)
-2*cos(x) + --------
               2    
$$\frac{3 \sin{\left(x \right)}}{2} - 2 \cos{\left(x \right)}$$
The graph
Derivative of (2*sin(x)+1,5*cos(x))