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log(x^2)/log(2)

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Derivative of:
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Identical expressions
log(x^ two)/log(two)
logarithm of (x squared ) divide by logarithm of (2)
logarithm of (x to the power of two) divide by logarithm of (two)
log(x2)/log(2)
logx2/log2
log(x²)/log(2)
log(x to the power of 2)/log(2)
logx^2/log2
log(x^2) divide by log(2)

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

Derivative of log(x^2)/log(2)

The solution

You have entered [src]

   / 2\
log\x /
-------
 log(2)

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

  /   / 2\\
d |log\x /|
--|-------|
dx\ log(2)/

\frac{d}{d x} \frac{\log{\left(x^{2} \right)}}{\log{\left(2 \right)}}

Transform

Detail solution

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

    4    
---------
 3       
x *log(2)

\frac{4}{x^{3} \log{\left(2 \right)}}

Simplify

The graph

Derivative of log(x^2)/log(2)