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Derivative of:
Derivative of (4-3*x)^7
Derivative of sqrt(x)-1/(sqrt(x)*2-x-1)
Derivative of -cos(t)
Derivative of 400/x
Identical expressions
sqrt(x)*(eight *x- five)
square root of (x) multiply by (8 multiply by x minus 5)
square root of (x) multiply by (eight multiply by x minus five)
√(x)*(8*x-5)
sqrt(x)(8x-5)
sqrtx8x-5
Similar expressions
sqrt(x)*(8*x+5)

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

Derivative of sqrt(x)(8x-5)

The solution

You have entered [src]

  ___          
\/ x *(8*x - 5)

$$\sqrt{x} \left(8 x - 5\right)$$

sqrt(x)*(8*x - 5)

Detail solution

Apply the product rule:

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

$f{\left(x \right)} = \sqrt{x}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
$g{\left(x \right)} = 8 x - 5$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
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 is: $8 \sqrt{x} + \frac{8 x - 5}{2 \sqrt{x}}$
Now simplify:

$\frac{24 x - 5}{2 \sqrt{x}}$

The answer is:

$\frac{24 x - 5}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    ___   8*x - 5
8*\/ x  + -------
              ___
          2*\/ x

$$8 \sqrt{x} + \frac{8 x - 5}{2 \sqrt{x}}$$

Simplify

The second derivative [src]

    -5 + 8*x
8 - --------
      4*x   
------------
     ___    
   \/ x

$$\frac{8 - \frac{8 x - 5}{4 x}}{\sqrt{x}}$$

Simplify

The third derivative [src]

  /     -5 + 8*x\
3*|-2 + --------|
  \       8*x   /
-----------------
        3/2      
       x

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

Simplify