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Derivative of:
Derivative of 5^-x
Derivative of x^2*sin(2*x-3)
Derivative of (x+1)^2*(x-5)-6
Derivative of log(11*x)
Identical expressions
four ^(eight *x- five)
4 to the power of (8 multiply by x minus 5)
four to the power of (eight multiply by x minus five)
4(8*x-5)
48*x-5
4^(8x-5)
4(8x-5)
48x-5
4^8x-5
Similar expressions
4^(8*x+5)

The derivative of the function/ 4^(8*x-5)

Derivative of 4^(8*x-5)

The solution

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 8*x - 5
4

$$4^{8 x - 5}$$

4^(8*x - 5)

Detail solution

Let $u = 8 x - 5$ .
$\frac{d}{d u} 4^{u} = 4^{u} \log{\left(4 \right)}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(8 x - 5\right)$ :
1. Differentiate $8 x - 5$ 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: $8$
  2. The derivative of the constant $-5$ is zero.
  The result is: $8$
The result of the chain rule is:

$8 \cdot 4^{8 x - 5} \log{\left(4 \right)}$
Now simplify:

$2^{16 x - 6} \log{\left(2 \right)}$

The answer is:

$2^{16 x - 6} \log{\left(2 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   8*x - 5       
8*4       *log(4)

$$8 \cdot 4^{8 x - 5} \log{\left(4 \right)}$$

Simplify

The second derivative [src]

 8*x    2   
4   *log (4)
------------
     16

$$\frac{4^{8 x} \log{\left(4 \right)}^{2}}{16}$$

Simplify

The third derivative [src]

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

$$\frac{4^{8 x} \log{\left(4 \right)}^{3}}{2}$$

Simplify