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Derivative of:
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Derivative of (2x+3)^2
Identical expressions
two *log(five *y- four)
2 multiply by logarithm of (5 multiply by y minus 4)
two multiply by logarithm of (five multiply by y minus four)
2log(5y-4)
2log5y-4
Similar expressions
2*log(5*y+4)

The derivative of the function/ 2*log(5*y-4)

Derivative of 2log(5y-4)

The solution

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2*log(5*y - 4)

$$2 \log{\left(5 y - 4 \right)}$$

2*log(5*y - 4)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 5 y - 4$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d y} \left(5 y - 4\right)$ :
  1. Differentiate $5 y - 4$ 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: $y$ goes to $1$
      So, the result is: $5$
    2. The derivative of the constant $-4$ is zero.
    The result is: $5$
  The result of the chain rule is:
  
  $\frac{5}{5 y - 4}$
So, the result is: $\frac{10}{5 y - 4}$
Now simplify:

$\frac{10}{5 y - 4}$

The answer is:

$\frac{10}{5 y - 4}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   10  
-------
5*y - 4

$$\frac{10}{5 y - 4}$$

Simplify

The second derivative [src]

    -50    
-----------
          2
(-4 + 5*y)

$$- \frac{50}{\left(5 y - 4\right)^{2}}$$

Simplify

The third derivative [src]

    500    
-----------
          3
(-4 + 5*y)

$$\frac{500}{\left(5 y - 4\right)^{3}}$$

Simplify

The graph

Derivative of 2*log(5*y-4)