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Derivative of:
Derivative of (x+5)/(x+1)
Derivative of x^(4/3)
Derivative of x*2^x
Derivative of x+log(x)
Integral of d{x}:
x*2^x
Equation:
x*2^x
Limit of the function:
x*2^x
Identical expressions
x* two ^x
x multiply by 2 to the power of x
x multiply by two to the power of x
x*2x
x2^x
x2x

The derivative of the function/ x*2^x

Derivative of x*2^x

The solution

You have entered [src]

   x
x*2

$$2^{x} x$$

x*2^x

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x$ goes to $1$
$g{\left(x \right)} = 2^{x}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. $\frac{d}{d x} 2^{x} = 2^{x} \log{\left(2 \right)}$
The result is: $2^{x} x \log{\left(2 \right)} + 2^{x}$
Now simplify:

$2^{x} \left(x \log{\left(2 \right)} + 1\right)$

The answer is:

$2^{x} \left(x \log{\left(2 \right)} + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 x      x       
2  + x*2 *log(2)

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

Simplify

The second derivative [src]

 x                      
2 *(2 + x*log(2))*log(2)

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

Simplify

The third derivative [src]

 x    2                  
2 *log (2)*(3 + x*log(2))

$$2^{x} \left(x \log{\left(2 \right)} + 3\right) \log{\left(2 \right)}^{2}$$

Simplify

The graph

Derivative of x*2^x