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Identical expressions
four *sqrt(x)- eight ^x^ two
4 multiply by square root of (x) minus 8 to the power of x squared
four multiply by square root of (x) minus eight to the power of x to the power of two
4*√(x)-8^x^2
4*sqrt(x)-8x2
4*sqrtx-8x2
4*sqrt(x)-8^x²
4*sqrt(x)-8 to the power of x to the power of 2
4sqrt(x)-8^x^2
4sqrt(x)-8x2
4sqrtx-8x2
4sqrtx-8^x^2
Similar expressions
4*sqrt(x)+8^x^2

The derivative of the function/ 4*sqrt(x)-8^x^2

Derivative of 4*sqrt(x)-8^x^2

The solution

You have entered [src]

           / 2\
    ___    \x /
4*\/ x  - 8

$$- 8^{x^{2}} + 4 \sqrt{x}$$

4*sqrt(x) - 8^(x^2)

Detail solution

Differentiate $- 8^{x^{2}} + 4 \sqrt{x}$ 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: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  So, the result is: $\frac{2}{\sqrt{x}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = x^{2}$ .
  2. $\frac{d}{d u} 8^{u} = 8^{u} \log{\left(8 \right)}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{2}$ :
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    The result of the chain rule is:
    
    $2 \cdot 8^{x^{2}} x \log{\left(8 \right)}$
  So, the result is: $- 2 \cdot 8^{x^{2}} x \log{\left(8 \right)}$
The result is: $- 2 \cdot 8^{x^{2}} x \log{\left(8 \right)} + \frac{2}{\sqrt{x}}$
Now simplify:

$- 6 \cdot 8^{x^{2}} x \log{\left(2 \right)} + \frac{2}{\sqrt{x}}$

The answer is:

$- 6 \cdot 8^{x^{2}} x \log{\left(2 \right)} + \frac{2}{\sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

             / 2\       
  2          \x /       
----- - 2*x*8    *log(8)
  ___                   
\/ x

$$- 2 \cdot 8^{x^{2}} x \log{\left(8 \right)} + \frac{2}{\sqrt{x}}$$

Simplify

The second derivative [src]

 /          / 2\             / 2\           \
 | 1        \x /             \x /  2    2   |
-|---- + 2*8    *log(8) + 4*8    *x *log (8)|
 | 3/2                                      |
 \x                                         /

$$- (4 \cdot 8^{x^{2}} x^{2} \log{\left(8 \right)}^{2} + 2 \cdot 8^{x^{2}} \log{\left(8 \right)} + \frac{1}{x^{\frac{3}{2}}})$$

Simplify

The third derivative [src]

               / 2\              / 2\           
  3            \x /    2         \x /  3    3   
------ - 12*x*8    *log (8) - 8*8    *x *log (8)
   5/2                                          
2*x

$$- 8 \cdot 8^{x^{2}} x^{3} \log{\left(8 \right)}^{3} - 12 \cdot 8^{x^{2}} x \log{\left(8 \right)}^{2} + \frac{3}{2 x^{\frac{5}{2}}}$$

Simplify

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Derivative of 4*sqrt(x)-8^x^2

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The solution