Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of y=5
Derivative of x^6-6x^10+12x
Derivative of log(1+e^x)
Derivative of (e^x+log(x))/(e^x-log(x))
Integral of d{x}:
ln^2x/1+x^2
Identical expressions
y=ln^ two x/ one +x^2
y equally ln squared x divide by 1 plus x squared
y equally ln to the power of two x divide by one plus x squared
y=ln2x/1+x2
y=ln²x/1+x²
y=ln to the power of 2x/1+x to the power of 2
y=ln^2x divide by 1+x^2
Similar expressions
y=ln^2x/1-x^2

The derivative of the function/ y=ln^2x/1+x^2

Derivative of y=ln^2x/1+x^2

The solution

You have entered [src]

   2        
log (x)    2
------- + x 
   1

$$x^{2} + \frac{\log{\left(x \right)}^{2}}{1}$$

log(x)^2/1 + x^2

Detail solution

Differentiate $x^{2} + \frac{\log{\left(x \right)}^{2}}{1}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \log{\left(x \right)}$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(x \right)}$ :
    1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
    The result of the chain rule is:
    
    $\frac{2 \log{\left(x \right)}}{x}$
  So, the result is: $\frac{2 \log{\left(x \right)}}{x}$
2. Apply the power rule: $x^{2}$ goes to $2 x$
The result is: $2 x + \frac{2 \log{\left(x \right)}}{x}$

The answer is:

$2 x + \frac{2 \log{\left(x \right)}}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      2*log(x)
2*x + --------
         x

$$2 x + \frac{2 \log{\left(x \right)}}{x}$$

Simplify

The second derivative [src]

  /    1    log(x)\
2*|1 + -- - ------|
  |     2      2  |
  \    x      x   /

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

Simplify

The third derivative [src]

2*(-3 + 2*log(x))
-----------------
         3       
        x

$$\frac{2 \left(2 \log{\left(x \right)} - 3\right)}{x^{3}}$$

Simplify

The graph

Derivative of y=ln^2x/1+x^2