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Identical expressions
y=(5x^ two -3x)/(3x- eight)
y equally (5x squared minus 3x) divide by (3x minus 8)
y equally (5x to the power of two minus 3x) divide by (3x minus eight)
y=(5x2-3x)/(3x-8)
y=5x2-3x/3x-8
y=(5x²-3x)/(3x-8)
y=(5x to the power of 2-3x)/(3x-8)
y=5x^2-3x/3x-8
y=(5x^2-3x) divide by (3x-8)
Similar expressions
y=(5x^2+3x)/(3x-8)
y=(5x^2-3x)/(3x+8)

The derivative of the function/ y=(5x^2-3x)/(3x-8)

Derivative of y=(5x^2-3x)/(3x-8)

The solution

You have entered [src]

   2      
5*x  - 3*x
----------
 3*x - 8

$$\frac{5 x^{2} - 3 x}{3 x - 8}$$

  /   2      \
d |5*x  - 3*x|
--|----------|
dx\ 3*x - 8  /

$$\frac{d}{d x} \frac{5 x^{2} - 3 x}{3 x - 8}$$

Transform

Detail solution

Apply the quotient rule, which is:

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

$f{\left(x \right)} = 5 x^{2} - 3 x$ and $g{\left(x \right)} = 3 x - 8$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $5 x^{2} - 3 x$ 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 a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $10 x$
  The result is: $10 x - 3$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $3 x - 8$ term by term:
  1. The derivative of the constant $-8$ 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: $3$
  The result is: $3$
Now plug in to the quotient rule:

$\frac{- 15 x^{2} + 9 x + \left(3 x - 8\right) \left(10 x - 3\right)}{\left(3 x - 8\right)^{2}}$
Now simplify:

$\frac{15 x^{2} - 80 x + 24}{9 x^{2} - 48 x + 64}$

The answer is:

$\frac{15 x^{2} - 80 x + 24}{9 x^{2} - 48 x + 64}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

              /   2      \
-3 + 10*x   3*\5*x  - 3*x/
--------- - --------------
 3*x - 8               2  
              (3*x - 8)

$$\frac{10 x - 3}{3 x - 8} - \frac{3 \cdot \left(5 x^{2} - 3 x\right)}{\left(3 x - 8\right)^{2}}$$

Simplify

The second derivative [src]

  /    3*(-3 + 10*x)   9*x*(-3 + 5*x)\
2*|5 - ------------- + --------------|
  |       -8 + 3*x                2  |
  \                     (-8 + 3*x)   /
--------------------------------------
               -8 + 3*x

$$\frac{2 \cdot \left(\frac{9 x \left(5 x - 3\right)}{\left(3 x - 8\right)^{2}} + 5 - \frac{3 \cdot \left(10 x - 3\right)}{3 x - 8}\right)}{3 x - 8}$$

Simplify

The third derivative [src]

   /     3*(-3 + 10*x)   9*x*(-3 + 5*x)\
18*|-5 + ------------- - --------------|
   |        -8 + 3*x                2  |
   \                      (-8 + 3*x)   /
----------------------------------------
                        2               
              (-8 + 3*x)

$$\frac{18 \left(- \frac{9 x \left(5 x - 3\right)}{\left(3 x - 8\right)^{2}} - 5 + \frac{3 \cdot \left(10 x - 3\right)}{3 x - 8}\right)}{\left(3 x - 8\right)^{2}}$$

Simplify

The graph

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Derivative of y=(5x^2-3x)/(3x-8)

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The solution