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Derivative of:
Derivative of 3^-x
Derivative of 6^(x^2-8x+28)
Derivative of 1-cost
Derivative of x^4/log(x)
Identical expressions
y=(x- three)/(x+ ten)
y equally (x minus 3) divide by (x plus 10)
y equally (x minus three) divide by (x plus ten)
y=x-3/x+10
y=(x-3) divide by (x+10)
Similar expressions
y=(x-3)/(x-10)
y=(x+3)/(x+10)

The derivative of the function/ y=(x-3)/(x+10)

Derivative of y=(x-3)/(x+10)

The solution

You have entered [src]

x - 3 
------
x + 10

$$\frac{x - 3}{x + 10}$$

(x - 3)/(x + 10)

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 $g{\left(x \right)} = x + 10$ .

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 $x + 10$ term by term:
  1. The derivative of the constant $10$ is zero.
  2. Apply the power rule: $x$ goes to $1$
  The result is: $1$
Now plug in to the quotient rule:

$\frac{13}{\left(x + 10\right)^{2}}$

The answer is:

$\frac{13}{\left(x + 10\right)^{2}}$

The first derivative [src]

  1        x - 3  
------ - ---------
x + 10           2
         (x + 10)

$$- \frac{x - 3}{\left(x + 10\right)^{2}} + \frac{1}{x + 10}$$

Simplify

The second derivative [src]

  /     -3 + x\
2*|-1 + ------|
  \     10 + x/
---------------
           2   
   (10 + x)

$$\frac{2 \left(\frac{x - 3}{x + 10} - 1\right)}{\left(x + 10\right)^{2}}$$

Simplify

3-я производная [src]

  /    -3 + x\
6*|1 - ------|
  \    10 + x/
--------------
          3   
  (10 + x)

$$\frac{6 \left(- \frac{x - 3}{x + 10} + 1\right)}{\left(x + 10\right)^{3}}$$

Simplify

The third derivative [src]

  /    -3 + x\
6*|1 - ------|
  \    10 + x/
--------------
          3   
  (10 + x)

$$\frac{6 \left(- \frac{x - 3}{x + 10} + 1\right)}{\left(x + 10\right)^{3}}$$

Simplify