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Derivative of y=(5x-3)*2^x

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           x
(5*x - 3)*2

$$2^{x} \left(5 x - 3\right)$$

(5*x - 3)*2^x

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = 5 x - 3$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $5 x - 3$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $5$
  2. The derivative of the constant $-3$ is zero.
  The result is: $5$
$g{\left(x \right)} = 2^{x}$ ; 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: $2^{x} \left(5 x - 3\right) \log{\left(2 \right)} + 5 \cdot 2^{x}$
Now simplify:

$2^{x} \left(\left(5 x - 3\right) \log{\left(2 \right)} + 5\right)$

The answer is:

$2^{x} \left(\left(5 x - 3\right) \log{\left(2 \right)} + 5\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   x    x                 
5*2  + 2 *(5*x - 3)*log(2)

$$2^{x} \left(5 x - 3\right) \log{\left(2 \right)} + 5 \cdot 2^{x}$$

Simplify

The second derivative [src]

 x                                
2 *(10 + (-3 + 5*x)*log(2))*log(2)

$$2^{x} \left(\left(5 x - 3\right) \log{\left(2 \right)} + 10\right) \log{\left(2 \right)}$$

Simplify

The third derivative [src]

 x    2                            
2 *log (2)*(15 + (-3 + 5*x)*log(2))

$$2^{x} \left(\left(5 x - 3\right) \log{\left(2 \right)} + 15\right) \log{\left(2 \right)}^{2}$$

Simplify