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Derivative of:
Derivative of x^2+cos(x)
Derivative of (x+1)^2*(x-5)-6
Derivative of log(11*x)
Derivative of e^x-2
Identical expressions
one /2sqrt(seven -2x)
1 divide by 2 square root of (7 minus 2x)
one divide by 2 square root of (seven minus 2x)
1/2√(7-2x)
1/2sqrt7-2x
1 divide by 2sqrt(7-2x)
Similar expressions
1/2sqrt(7+2x)

The derivative of the function/ 1/2sqrt(7-2x)

Derivative of 1/2sqrt(7-2x)

The solution

You have entered [src]

  _________
\/ 7 - 2*x 
-----------
     2

$$\frac{\sqrt{7 - 2 x}}{2}$$

sqrt(7 - 2*x)/2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 7 - 2 x$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(7 - 2 x\right)$ :
  1. Differentiate $7 - 2 x$ term by term:
    1. The derivative of the constant $7$ is zero.
    2. 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: $-2$
    The result is: $-2$
  The result of the chain rule is:
  
  $- \frac{1}{\sqrt{7 - 2 x}}$
So, the result is: $- \frac{1}{2 \sqrt{7 - 2 x}}$

The answer is:

$- \frac{1}{2 \sqrt{7 - 2 x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     -1      
-------------
    _________
2*\/ 7 - 2*x

$$- \frac{1}{2 \sqrt{7 - 2 x}}$$

Simplify

The second derivative [src]

     -1       
--------------
           3/2
2*(7 - 2*x)

$$- \frac{1}{2 \left(7 - 2 x\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

     -3       
--------------
           5/2
2*(7 - 2*x)

$$- \frac{3}{2 \left(7 - 2 x\right)^{\frac{5}{2}}}$$

Simplify