Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (3x-1)/(2x+5)
Derivative of ln(x^2+16)
Derivative of y=x³-4x²-3x
Derivative of (3x²+1)³
Identical expressions
ln(x^ two + sixteen)
ln(x squared plus 16)
ln(x to the power of two plus sixteen)
ln(x2+16)
lnx2+16
ln(x²+16)
ln(x to the power of 2+16)
lnx^2+16
Similar expressions
ln(x^2-16)

The derivative of the function/ ln(x^2+16)

Derivative of ln(x^2+16)

The solution

You have entered [src]

   / 2     \
log\x  + 16/

$$\log{\left(x^{2} + 16 \right)}$$

log(x^2 + 16)

Detail solution

Let $u = x^{2} + 16$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} + 16\right)$ :
1. Differentiate $x^{2} + 16$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $16$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$\frac{2 x}{x^{2} + 16}$
Now simplify:

$\frac{2 x}{x^{2} + 16}$

The answer is:

$\frac{2 x}{x^{2} + 16}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  2*x  
-------
 2     
x  + 16

$$\frac{2 x}{x^{2} + 16}$$

Simplify

The second derivative [src]

  /         2 \
  |      2*x  |
2*|1 - -------|
  |          2|
  \    16 + x /
---------------
          2    
    16 + x

$$\frac{2 \left(- \frac{2 x^{2}}{x^{2} + 16} + 1\right)}{x^{2} + 16}$$

Simplify

The third derivative [src]

    /          2 \
    |       4*x  |
4*x*|-3 + -------|
    |           2|
    \     16 + x /
------------------
             2    
    /      2\     
    \16 + x /

$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} + 16} - 3\right)}{\left(x^{2} + 16\right)^{2}}$$

Simplify

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of ln(x^2+16)

The graph:

Piecewise:

The solution