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The derivative of the function/ 4cosx+3sinx+2

Derivative of 4cosx+3sinx+2

The solution

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4*cos(x) + 3*sin(x) + 2

$$\left(3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}\right) + 2$$

4*cos(x) + 3*sin(x) + 2

Detail solution

Differentiate $\left(3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}\right) + 2$ term by term:
1. Differentiate $3 \sin{\left(x \right)} + 4 \cos{\left(x \right)}$ 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 cosine is negative sine:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
    So, the result is: $- 4 \sin{\left(x \right)}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of sine is cosine:
      
      $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
    So, the result is: $3 \cos{\left(x \right)}$
  The result is: $- 4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$
2. The derivative of the constant $2$ is zero.
The result is: $- 4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$

The answer is:

$- 4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-4*sin(x) + 3*cos(x)

$$- 4 \sin{\left(x \right)} + 3 \cos{\left(x \right)}$$

Simplify

The second derivative [src]

-(3*sin(x) + 4*cos(x))

$$- (3 \sin{\left(x \right)} + 4 \cos{\left(x \right)})$$

Simplify

The third derivative [src]

-3*cos(x) + 4*sin(x)

$$4 \sin{\left(x \right)} - 3 \cos{\left(x \right)}$$

Simplify