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Derivative of:
Derivative of e^x^x
Derivative of 5e^x
Derivative of 3*(2-x)^6
Derivative of (-2)/x^2
Identical expressions
log(x)/log(two)-3x^ two
logarithm of (x) divide by logarithm of (2) minus 3x squared
logarithm of (x) divide by logarithm of (two) minus 3x to the power of two
log(x)/log(2)-3x2
logx/log2-3x2
log(x)/log(2)-3x²
log(x)/log(2)-3x to the power of 2
logx/log2-3x^2
log(x) divide by log(2)-3x^2
Similar expressions
log(x)/log(2)+3x^2

The derivative of the function/ log(x)/log(2)-3x^2

Derivative of log(x)/log(2)-3x^2

The solution

You have entered [src]

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

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

log(x)/log(2) - 3*x^2

Detail solution

Differentiate $- 3 x^{2} + \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}$ 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: $\frac{1}{x \log{\left(2 \right)}}$
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: $- 6 x$
The result is: $- 6 x + \frac{1}{x \log{\left(2 \right)}}$

The answer is:

$- 6 x + \frac{1}{x \log{\left(2 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          1    
-6*x + --------
       x*log(2)

$$- 6 x + \frac{1}{x \log{\left(2 \right)}}$$

Simplify

The second derivative [src]

 /        1    \
-|6 + ---------|
 |     2       |
 \    x *log(2)/

$$- (6 + \frac{1}{x^{2} \log{\left(2 \right)}})$$

Simplify

The third derivative [src]

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

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

Simplify