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4*cos(x)-2*sin(x)

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Derivative of:
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Identical expressions
four *cos(x)- two *sin(x)
4 multiply by co sinus of e of (x) minus 2 multiply by sinus of (x)
four multiply by co sinus of e of (x) minus two multiply by sinus of (x)
4cos(x)-2sin(x)
4cosx-2sinx
Similar expressions
4*cos(x)+2*sin(x)
4*cosx-2*sinx

The derivative of the function/ 4*cos(x)-2*sin(x)

Derivative of 4cos(x)-2sin(x)

The solution

You have entered [src]

4*cos(x) - 2*sin(x)

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

d                      
--(4*cos(x) - 2*sin(x))
dx

$$\frac{d}{d x} \left(- 2 \sin{\left(x \right)} + 4 \cos{\left(x \right)}\right)$$

Transform

Detail solution

Differentiate $- 2 \sin{\left(x \right)} + 4 \cos{\left(x \right)}$ 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 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: $2 \cos{\left(x \right)}$
  So, the result is: $- 2 \cos{\left(x \right)}$
The result is: $- 4 \sin{\left(x \right)} - 2 \cos{\left(x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-4*sin(x) - 2*cos(x)

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

Simplify

The second derivative [src]

2*(-2*cos(x) + sin(x))

$$2 \left(\sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)$$

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of 4*cos(x)-2*sin(x)