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Derivative of:
Derivative of 4/x^3
Derivative of (x+3)^2*(x+5)-1
Derivative of x^3+2
Derivative of x^(-2)
Identical expressions
logx- one *(x^ two)
logarithm of x minus 1 multiply by (x squared )
logarithm of x minus one multiply by (x to the power of two)
logx-1*(x2)
logx-1*x2
logx-1*(x²)
logx-1*(x to the power of 2)
logx-1(x^2)
logx-1(x2)
logx-1x2
logx-1x^2
Similar expressions
logx+1*(x^2)

The derivative of the function/ logx-1*(x^2)

Derivative of logx-1*(x^2)

The solution

You have entered [src]

          2
log(x) - x

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

log(x) - x^2

Detail solution

Differentiate $- x^{2} + \log{\left(x \right)}$ 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: $x^{2}$ goes to $2 x$
  So, the result is: $- 2 x$
The result is: $- 2 x + \frac{1}{x}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1      
- - 2*x
x

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

2 
--
 3
x

$$\frac{2}{x^{3}}$$

Simplify