Derivative of 2^x(x+10)

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 x         
2 *(x + 10)

$$2^{x} \left(x + 10\right)$$

2^x*(x + 10)

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = 2^{x}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. $\frac{d}{d x} 2^{x} = 2^{x} \log{\left(2 \right)}$
$g{\left(x \right)} = x + 10$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 10$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $10$ is zero.
  The result is: $1$
The result is: $2^{x} \left(x + 10\right) \log{\left(2 \right)} + 2^{x}$
Now simplify:

$2^{x} \left(\left(x + 10\right) \log{\left(2 \right)} + 1\right)$

The answer is:

$2^{x} \left(\left(x + 10\right) \log{\left(2 \right)} + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 x    x                
2  + 2 *(x + 10)*log(2)

$$2^{x} \left(x + 10\right) \log{\left(2 \right)} + 2^{x}$$

Simplify

The second derivative [src]

 x                             
2 *(2 + (10 + x)*log(2))*log(2)

$$2^{x} \left(\left(x + 10\right) \log{\left(2 \right)} + 2\right) \log{\left(2 \right)}$$

Simplify

The third derivative [src]

 x    2                         
2 *log (2)*(3 + (10 + x)*log(2))

$$2^{x} \left(\left(x + 10\right) \log{\left(2 \right)} + 3\right) \log{\left(2 \right)}^{2}$$

Simplify