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函数导数/ 2cosx-2sinx

导数 2cosx-2sinx

解答

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

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

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

Detail solution

Differentiate $- 2 \sin{\left(x \right)} + 2 \cos{\left(x \right)}$ 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: $- 2 \sin{\left(x \right)}$
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: $- 2 \cos{\left(x \right)}$
The result is: $- 2 \sin{\left(x \right)} - 2 \cos{\left(x \right)}$
Now simplify:

$- 2 \sqrt{2} \sin{\left(x + \frac{\pi}{4} \right)}$

The answer is:

$- 2 \sqrt{2} \sin{\left(x + \frac{\pi}{4} \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify