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Derivative of:
Derivative of tan(x/2)
Derivative of (x^2)
Derivative of sin(x)/2
Derivative of lnx
Identical expressions
four ^x+2sin(x)
4 to the power of x plus 2 sinus of (x)
four to the power of x plus 2 sinus of (x)
4x+2sin(x)
4x+2sinx
4^x+2sinx
Similar expressions
4^x-2sin(x)
4^x+2sinx

The derivative of the function/ 4^x+2sin(x)

Derivative of 4^x+2sin(x)

The solution

You have entered [src]

 x           
4  + 2*sin(x)

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

4^x + 2*sin(x)

Detail solution

Differentiate $4^{x} + 2 \sin{\left(x \right)}$ term by term:
1. $\frac{d}{d x} 4^{x} = 4^{x} \log{\left(4 \right)}$
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: $4^{x} \log{\left(4 \right)} + 2 \cos{\left(x \right)}$
Now simplify:

$2 \cdot 4^{x} \log{\left(2 \right)} + 2 \cos{\left(x \right)}$

The answer is:

$2 \cdot 4^{x} \log{\left(2 \right)} + 2 \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

            x       
2*cos(x) + 4 *log(4)

$$4^{x} \log{\left(4 \right)} + 2 \cos{\left(x \right)}$$

Simplify

The second derivative [src]

             x    2   
-2*sin(x) + 4 *log (4)

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

Simplify

The third derivative [src]

             x    3   
-2*cos(x) + 4 *log (4)

$$4^{x} \log{\left(4 \right)}^{3} - 2 \cos{\left(x \right)}$$

Simplify