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The derivative of the function/ 2x*lnx-x*ln49

Derivative of 2xlnx-xln49

The solution

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2*x*log(x) - x*log(49)

$$2 x \log{\left(x \right)} - x \log{\left(49 \right)}$$

d                         
--(2*x*log(x) - x*log(49))
dx

$$\frac{d}{d x} \left(2 x \log{\left(x \right)} - x \log{\left(49 \right)}\right)$$

Transform

Detail solution

Differentiate $2 x \log{\left(x \right)} - x \log{\left(49 \right)}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the product rule:
    
    $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
    
    $f{\left(x \right)} = x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
    1. Apply the power rule: $x$ goes to $1$
    $g{\left(x \right)} = \log{\left(x \right)}$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
    1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
    The result is: $\log{\left(x \right)} + 1$
  So, the result is: $2 \log{\left(x \right)} + 2$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. 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: $\log{\left(49 \right)}$
  So, the result is: $- \log{\left(49 \right)}$
The result is: $2 \log{\left(x \right)} - \log{\left(49 \right)} + 2$

The answer is:

$2 \log{\left(x \right)} - \log{\left(49 \right)} + 2$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2 - log(49) + 2*log(x)

$$2 \log{\left(x \right)} - \log{\left(49 \right)} + 2$$

Simplify

The second derivative [src]

2
-
x

$$\frac{2}{x}$$

Simplify

The third derivative [src]

-2 
---
  2
 x

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

Simplify

The graph

Derivative of 2x*lnx-x*ln49