Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 3x^2-5x+5
Derivative of (2*x-1)^2
Derivative of (2*e)^cos(log(6*x-1))^(2)
Derivative of 1/tg(x)
Identical expressions
y=sqrt(three *x- fourteen)
y equally square root of (3 multiply by x minus 14)
y equally square root of (three multiply by x minus fourteen)
y=√(3*x-14)
y=sqrt(3x-14)
y=sqrt3x-14
Similar expressions
y=sqrt(3*x+14)
y=sqrt3x-14

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

Derivative of y=sqrt(3*x-14)

The solution

You have entered [src]

  __________
\/ 3*x - 14

$$\sqrt{3 x - 14}$$

sqrt(3*x - 14)

Detail solution

Let $u = 3 x - 14$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x - 14\right)$ :
1. Differentiate $3 x - 14$ 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: $3$
  2. The derivative of the constant $-14$ is zero.
  The result is: $3$
The result of the chain rule is:

$\frac{3}{2 \sqrt{3 x - 14}}$
Now simplify:

$\frac{3}{2 \sqrt{3 x - 14}}$

The answer is:

$\frac{3}{2 \sqrt{3 x - 14}}$

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(3*x-14)