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x*2^x
The derivative of the function/ x*2^x

Derivative of x*2^x

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   x
x*2
2xx2^{x} x 
x*2^x
Detail solution

  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\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(x)=xf{\left(x \right)} = x; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Apply the power rule: xx goes to 11

    g(x)=2xg{\left(x \right)} = 2^{x}; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. ddx2x=2xlog⁡(2)\frac{d}{d x} 2^{x} = 2^{x} \log{\left(2 \right)}

    The result is: 2xxlog⁡(2)+2x2^{x} x \log{\left(2 \right)} + 2^{x}

  2. Now simplify:

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

The answer is:

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

The graph
02468-8-6-4-2-101020000-10000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 x      x       
2  + x*2 *log(2)
2xxlog⁡(2)+2x2^{x} x \log{\left(2 \right)} + 2^{x}
Simplify
The second derivative [src] 
 x                      
2 *(2 + x*log(2))*log(2)
2x(xlog⁡(2)+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))
2x(xlog⁡(2)+3)log⁡(2)22^{x} \left(x \log{\left(2 \right)} + 3\right) \log{\left(2 \right)}^{2}
Simplify
The graph
Derivative of x*2^x
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