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Derivative of:
Derivative of 5e^x
Derivative of 3*x^2*e^x
Derivative of 3*(2-x)^6
Derivative of 1/(2x)
Identical expressions
2e^x- three • four ^x+ five
2e to the power of x minus 3•4 to the power of x plus 5
2e to the power of x minus three • four to the power of x plus five
2ex-3•4x+5
Similar expressions
2e^x-3•4^x-5
2e^x+3•4^x+5

The derivative of the function/ 2e^x-3•4^x+5

Derivative of 2e^x-3•4^x+5

The solution

You have entered [src]

   x      x    
2*e  - 3*4  + 5

$$- 3 \cdot 4^{x} + 2 e^{x} + 5$$

d /   x      x    \
--\2*e  - 3*4  + 5/
dx

$$\frac{d}{d x} \left(- 3 \cdot 4^{x} + 2 e^{x} + 5\right)$$

Transform

Detail solution

Differentiate $- 3 \cdot 4^{x} + 2 e^{x} + 5$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $e^{x}$ is itself.
  So, the result is: $2 e^{x}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. $\frac{d}{d x} 4^{x} = 4^{x} \log{\left(4 \right)}$
    So, the result is: $3 \cdot 4^{x} \log{\left(4 \right)}$
  So, the result is: $- 3 \cdot 4^{x} \log{\left(4 \right)}$
3. The derivative of the constant $5$ is zero.
The result is: $- 3 \cdot 4^{x} \log{\left(4 \right)} + 2 e^{x}$
Now simplify:

$- 6 \cdot 4^{x} \log{\left(2 \right)} + 2 e^{x}$

The answer is:

$- 6 \cdot 4^{x} \log{\left(2 \right)} + 2 e^{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   x      x       
2*e  - 3*4 *log(4)

$$- 3 \cdot 4^{x} \log{\left(4 \right)} + 2 e^{x}$$

Simplify

The second derivative [src]

   x      x    2   
2*e  - 3*4 *log (4)

$$- 3 \cdot 4^{x} \log{\left(4 \right)}^{2} + 2 e^{x}$$

Simplify

The third derivative [src]

   x      x    3   
2*e  - 3*4 *log (4)

$$- 3 \cdot 4^{x} \log{\left(4 \right)}^{3} + 2 e^{x}$$

Simplify

The graph

Derivative of 2e^x-3•4^x+5