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log(x^2+5)
The derivative of the function/ log(x^2+5)

Derivative of log(x^2+5)

Function f() - derivative -N order at the point
v

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The solution

You have entered [src] 
   / 2    \
log\x  + 5/
log⁡(x2+5)\log{\left(x^{2} + 5 \right)} 
log(x^2 + 5)
Detail solution

  1. Let u=x2+5u = x^{2} + 5.

  2. The derivative of log⁡(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddx(x2+5)\frac{d}{d x} \left(x^{2} + 5\right):

    1. Differentiate x2+5x^{2} + 5 term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      2. The derivative of the constant 55 is zero.

      The result is: 2x2 x

    The result of the chain rule is:

    2xx2+5\frac{2 x}{x^{2} + 5}

  4. Now simplify:

    2xx2+5\frac{2 x}{x^{2} + 5}

The answer is:

2xx2+5\frac{2 x}{x^{2} + 5}

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 2*x  
------
 2    
x  + 5
2xx2+5\frac{2 x}{x^{2} + 5}
Simplify
The second derivative [src] 
  /        2 \
  |     2*x  |
2*|1 - ------|
  |         2|
  \    5 + x /
--------------
         2    
    5 + x
2(−2x2x2+5+1)x2+5\frac{2 \left(- \frac{2 x^{2}}{x^{2} + 5} + 1\right)}{x^{2} + 5}
Simplify
The third derivative [src] 
    /         2 \
    |      4*x  |
4*x*|-3 + ------|
    |          2|
    \     5 + x /
-----------------
            2    
    /     2\     
    \5 + x /
4x(4x2x2+5−3)(x2+5)2\frac{4 x \left(\frac{4 x^{2}}{x^{2} + 5} - 3\right)}{\left(x^{2} + 5\right)^{2}}
Simplify
The graph
Derivative of log(x^2+5)
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