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The derivative of the function/ 2e^(x)-cosx

Derivative of 2e^(x)-cosx

The solution

You have entered [src]

   x         
2*e  - cos(x)

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

d /   x         \
--\2*e  - cos(x)/
dx

$$\frac{d}{d x} \left(2 e^{x} - \cos{\left(x \right)}\right)$$

Transform

Detail solution

Differentiate $2 e^{x} - \cos{\left(x \right)}$ 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 $e^{x}$ is itself.
  So, the result is: $2 e^{x}$
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:
    
    $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
  So, the result is: $\sin{\left(x \right)}$
The result is: $2 e^{x} + \sin{\left(x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   x         
2*e  + sin(x)

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

Simplify

The second derivative [src]

   x         
2*e  + cos(x)

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

Simplify

The third derivative [src]

             x
-sin(x) + 2*e

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

Simplify

The graph

Derivative of 2e^(x)-cosx