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Derivative of:
Derivative of (x+3)^4
Derivative of (x^2-x)*(x^3+x)
Derivative of (x-2)^4
Derivative of (x^2-1)*(x^4+2)
Identical expressions
y=(x- three)/(2x+ seven)
y equally (x minus 3) divide by (2x plus 7)
y equally (x minus three) divide by (2x plus seven)
y=x-3/2x+7
y=(x-3) divide by (2x+7)
Similar expressions
y=(x-3)/(2x-7)
y=(x+3)/(2x+7)

The derivative of the function/ y=(x-3)/(2x+7)

Derivative of y=(x-3)/(2x+7)

The solution

You have entered [src]

 x - 3 
-------
2*x + 7

$$\frac{x - 3}{2 x + 7}$$

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

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = x - 3$ and $g{\left(x \right)} = 2 x + 7$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $x - 3$ term by term:
  1. The derivative of the constant $-3$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $2 x + 7$ 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: $2$
Now plug in to the quotient rule:

$\frac{13}{\left(2 x + 7\right)^{2}}$

The answer is:

$\frac{13}{\left(2 x + 7\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  /     2*(-3 + x)\
4*|-1 + ----------|
  \      7 + 2*x  /
-------------------
              2    
     (7 + 2*x)

$$\frac{4 \left(\frac{2 \left(x - 3\right)}{2 x + 7} - 1\right)}{\left(2 x + 7\right)^{2}}$$

Simplify

The third derivative [src]

   /    2*(-3 + x)\
24*|1 - ----------|
   \     7 + 2*x  /
-------------------
              3    
     (7 + 2*x)

$$\frac{24 \left(- \frac{2 \left(x - 3\right)}{2 x + 7} + 1\right)}{\left(2 x + 7\right)^{3}}$$

Simplify

The graph

Derivative of y=(x-3)/(2x+7)