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y=sqrt(3x-14)
The derivative of the function/ y=sqrt(3x-14)

Derivative of y=sqrt(3x-14)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  __________
\/ 3*x - 14
$$\sqrt{3 x - 14}$$ 
d /  __________\
--\\/ 3*x - 14 /
dx
$$\frac{d}{d x} \sqrt{3 x - 14}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate 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: goes to

        So, the result is:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      3       
--------------
    __________
2*\/ 3*x - 14
$$\frac{3}{2 \sqrt{3 x - 14}}$$
Simplify
The second derivative [src] 
      -9        
----------------
             3/2
4*(-14 + 3*x)
$$- \frac{9}{4 \left(3 x - 14\right)^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
       81       
----------------
             5/2
8*(-14 + 3*x)
$$\frac{81}{8 \left(3 x - 14\right)^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of y=sqrt(3x-14)
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