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y=lnx-3x^2+5x+2

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Identical expressions
y=lnx-3x^ two +5x+ two
y equally lnx minus 3x squared plus 5x plus 2
y equally lnx minus 3x to the power of two plus 5x plus two
y=lnx-3x2+5x+2
y=lnx-3x²+5x+2
y=lnx-3x to the power of 2+5x+2
Similar expressions
y=lnx+3x^2+5x+2
y=lnx-3x^2-5x+2
y=lnx-3x^2+5x-2

The derivative of the function/ y=lnx-3x^2+5x+2

Derivative of y=lnx-3x^2+5x+2

The solution

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            2          
log(x) - 3*x  + 5*x + 2

$$\left(5 x + \left(- 3 x^{2} + \log{\left(x \right)}\right)\right) + 2$$

log(x) - 3*x^2 + 5*x + 2

Detail solution

Differentiate $\left(5 x + \left(- 3 x^{2} + \log{\left(x \right)}\right)\right) + 2$ term by term:
1. Differentiate $5 x + \left(- 3 x^{2} + \log{\left(x \right)}\right)$ term by term:
  1. Differentiate $- 3 x^{2} + \log{\left(x \right)}$ 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: $- 6 x$
    The result is: $- 6 x + \frac{1}{x}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $5$
  The result is: $- 6 x + 5 + \frac{1}{x}$
2. The derivative of the constant $2$ is zero.
The result is: $- 6 x + 5 + \frac{1}{x}$

The answer is:

$- 6 x + 5 + \frac{1}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    1      
5 + - - 6*x
    x

$$- 6 x + 5 + \frac{1}{x}$$

Simplify

The second derivative [src]

 /    1 \
-|6 + --|
 |     2|
 \    x /

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

Simplify

The third derivative [src]

2 
--
 3
x

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

Simplify

The graph

Derivative of y=lnx-3x^2+5x+2