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1,5x^2-27x+42lnx-10

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Derivative of:
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Identical expressions
one ,5x^ two -27x+42lnx- ten
1,5x squared minus 27x plus 42lnx minus 10
one ,5x to the power of two minus 27x plus 42lnx minus ten
1,5x2-27x+42lnx-10
1,5x²-27x+42lnx-10
1,5x to the power of 2-27x+42lnx-10
Similar expressions
1,5x^2-27x-42lnx-10
1,5x^2-27x+42lnx+10
1,5x^2+27x+42lnx-10

The derivative of the function/ 1,5x^2-27x+42lnx-10

Derivative of 1,5x^2-27x+42lnx-10

The solution

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   2                        
3*x                         
---- - 27*x + 42*log(x) - 10
 2

$$\left(\left(\frac{3 x^{2}}{2} - 27 x\right) + 42 \log{\left(x \right)}\right) - 10$$

3*x^2/2 - 27*x + 42*log(x) - 10

Detail solution

Differentiate $\left(\left(\frac{3 x^{2}}{2} - 27 x\right) + 42 \log{\left(x \right)}\right) - 10$ term by term:
1. Differentiate $\left(\frac{3 x^{2}}{2} - 27 x\right) + 42 \log{\left(x \right)}$ term by term:
  1. Differentiate $\frac{3 x^{2}}{2} - 27 x$ term by term:
    1. 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: $3 x$
    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: $-27$
    The result is: $3 x - 27$
  2. 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: $\frac{42}{x}$
  The result is: $3 x - 27 + \frac{42}{x}$
2. The derivative of the constant $-10$ is zero.
The result is: $3 x - 27 + \frac{42}{x}$

The answer is:

$3 x - 27 + \frac{42}{x}$

The graph

Plot the graph f(x)

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The first derivative [src]

            42
-27 + 3*x + --
            x

$$3 x - 27 + \frac{42}{x}$$

Simplify

The second derivative [src]

  /    14\
3*|1 - --|
  |     2|
  \    x /

$$3 \left(1 - \frac{14}{x^{2}}\right)$$

Simplify

The third derivative [src]

84
--
 3
x

$$\frac{84}{x^{3}}$$

Simplify

The graph

Derivative of 1,5x^2-27x+42lnx-10