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Identical expressions
ten x-ln(x+ ten)^10
10x minus ln(x plus 10) to the power of 10
ten x minus ln(x plus ten) to the power of 10
10x-ln(x+10)10
10x-lnx+1010
10x-lnx+10^10
Similar expressions
10x+ln(x+10)^10
10x-ln(x-10)^10

The derivative of the function/ 10x-ln(x+10)^10

Derivative of 10x-ln(x+10)^10

The solution

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          10        
10*x - log  (x + 10)

$$10 x - \log{\left(x + 10 \right)}^{10}$$

10*x - log(x + 10)^10

Detail solution

Differentiate $10 x - \log{\left(x + 10 \right)}^{10}$ 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: $x$ goes to $1$
  So, the result is: $10$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \log{\left(x + 10 \right)}$ .
  2. Apply the power rule: $u^{10}$ goes to $10 u^{9}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(x + 10 \right)}$ :
    1. Let $u = x + 10$ .
    2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 10\right)$ :
      1. Differentiate $x + 10$ term by term:
        
        Apply the power rule: $x$ goes to $1$
        
        The derivative of the constant $10$ is zero.
        
        The result is: $1$
      The result of the chain rule is:
      
      $\frac{1}{x + 10}$
    The result of the chain rule is:
    
    $\frac{10 \log{\left(x + 10 \right)}^{9}}{x + 10}$
  So, the result is: $- \frac{10 \log{\left(x + 10 \right)}^{9}}{x + 10}$
The result is: $10 - \frac{10 \log{\left(x + 10 \right)}^{9}}{x + 10}$
Now simplify:

$\frac{10 \left(x - \log{\left(x + 10 \right)}^{9} + 10\right)}{x + 10}$

The answer is:

$\frac{10 \left(x - \log{\left(x + 10 \right)}^{9} + 10\right)}{x + 10}$

The first derivative [src]

           9        
     10*log (x + 10)
10 - ---------------
          x + 10

$$10 - \frac{10 \log{\left(x + 10 \right)}^{9}}{x + 10}$$

Simplify

The second derivative [src]

      8                           
10*log (10 + x)*(-9 + log(10 + x))
----------------------------------
                    2             
            (10 + x)

$$\frac{10 \left(\log{\left(x + 10 \right)} - 9\right) \log{\left(x + 10 \right)}^{8}}{\left(x + 10\right)^{2}}$$

Simplify

The third derivative [src]

      7         /           2                         \
10*log (10 + x)*\-72 - 2*log (10 + x) + 27*log(10 + x)/
-------------------------------------------------------
                               3                       
                       (10 + x)

$$\frac{10 \left(- 2 \log{\left(x + 10 \right)}^{2} + 27 \log{\left(x + 10 \right)} - 72\right) \log{\left(x + 10 \right)}^{7}}{\left(x + 10\right)^{3}}$$

Simplify

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Derivative of 10x-ln(x+10)^10

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