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Derivative of (ln(x)/ln(4))-4*x^2

You have entered [src]

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

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

log(x)/log(4) - 4*x^2

Detail solution

Differentiate $- 4 x^{2} + \frac{\log{\left(x \right)}}{\log{\left(4 \right)}}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  So, the result is: $\frac{1}{x \log{\left(4 \right)}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  So, the result is: $- 8 x$
The result is: $- 8 x + \frac{1}{x \log{\left(4 \right)}}$
Now simplify:

$\frac{1 - \log{\left(2^{16 x^{2}} \right)}}{x \log{\left(4 \right)}}$

The answer is:

$\frac{1 - \log{\left(2^{16 x^{2}} \right)}}{x \log{\left(4 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          1    
-8*x + --------
       x*log(4)

$$- 8 x + \frac{1}{x \log{\left(4 \right)}}$$

Simplify

The second derivative [src]

 /        1    \
-|8 + ---------|
 |     2       |
 \    x *log(4)/

$$- (8 + \frac{1}{x^{2} \log{\left(4 \right)}})$$

Simplify

The third derivative [src]

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

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

Simplify