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Derivative of:
Derivative of x^-6
Derivative of -x/2
Derivative of x*2^x
Derivative of 2^(1/x)
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)=lnx- three x^3
f(x) equally lnx minus 3x cubed
f(x) equally lnx minus three x cubed
f(x)=lnx-3x3
fx=lnx-3x3
f(x)=lnx-3x³
f(x)=lnx-3x to the power of 3
fx=lnx-3x^3
Similar expressions
f(x)=lnx+3x^3

The derivative of the function/ f(x)=lnx-3x^3

Derivative of f(x)=lnx-3x^3

The solution

You have entered [src]

            3
log(x) - 3*x

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

log(x) - 3*x^3

Detail solution

Differentiate $- 3 x^{3} + \log{\left(x \right)}$ term by term:
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $- 9 x^{2}$
The result is: $- 9 x^{2} + \frac{1}{x}$
Now simplify:

$\frac{1 - 9 x^{3}}{x}$

The answer is:

$\frac{1 - 9 x^{3}}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1      2
- - 9*x 
x

$$- 9 x^{2} + \frac{1}{x}$$

Simplify

The second derivative [src]

 /1        \
-|-- + 18*x|
 | 2       |
 \x        /

$$- (18 x + \frac{1}{x^{2}})$$

Simplify

The third derivative [src]

  /     1 \
2*|-9 + --|
  |      3|
  \     x /

$$2 \left(-9 + \frac{1}{x^{3}}\right)$$

Simplify