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Derivative of:
Derivative of (x+1)/x
Derivative of sqrt(cos(x))
Derivative of sen2x
Derivative of ln(ln(x))
Graphing y =:
x^2/2x+7
Identical expressions
y=x^ two /2x+ seven
y equally x squared divide by 2x plus 7
y equally x to the power of two divide by 2x plus seven
y=x2/2x+7
y=x²/2x+7
y=x to the power of 2/2x+7
y=x^2 divide by 2x+7
Similar expressions
y=x^2/2x-7

The derivative of the function/ y=x^2/2x+7

Derivative of y=x^2/2x+7

The solution

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 2      
x       
--*x + 7
2

$$x \frac{x^{2}}{2} + 7$$

(x^2/2)*x + 7

Detail solution

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

The answer is:

$\frac{3 x^{2}}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

$$\frac{x^{2}}{2} + x^{2}$$

Simplify

The second derivative [src]

3*x

$$3 x$$

Simplify

The third derivative [src]

$$3$$

Simplify

The graph

Derivative of y=x^2/2x+7