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Derivative of 3lnx
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Derivative of y=log5(3x^2-5)
Identical expressions
y=log five (3x^ two -5)
y equally logarithm of 5(3x squared minus 5)
y equally logarithm of five (3x to the power of two minus 5)
y=log5(3x2-5)
y=log53x2-5
y=log5(3x²-5)
y=log5(3x to the power of 2-5)
y=log53x^2-5
Similar expressions
y=log5(3x^2+5)
y=log(5)*(3x^2-5)

The derivative of the function/ y=log5(3x^2-5)

Derivative of y=log5(3x^2-5)

The solution

You have entered [src]

   /   2    \
log\3*x  - 5/
-------------
    log(5)

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

  /   /   2    \\
d |log\3*x  - 5/|
--|-------------|
dx\    log(5)   /

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

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 3 x^{2} - 5$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x^{2} - 5\right)$ :
  1. Differentiate $3 x^{2} - 5$ 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: $6 x$
    2. The derivative of the constant $\left(-1\right) 5$ is zero.
    The result is: $6 x$
  The result of the chain rule is:
  
  $\frac{6 x}{3 x^{2} - 5}$
So, the result is: $\frac{6 x}{\left(3 x^{2} - 5\right) \log{\left(5 \right)}}$
Now simplify:

$\frac{6 x}{\left(3 x^{2} - 5\right) \log{\left(5 \right)}}$

The answer is:

$\frac{6 x}{\left(3 x^{2} - 5\right) \log{\left(5 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       6*x       
-----------------
/   2    \       
\3*x  - 5/*log(5)

$$\frac{6 x}{\left(3 x^{2} - 5\right) \log{\left(5 \right)}}$$

Simplify

The second derivative [src]

   /           2  \
   |        6*x   |
-6*|-1 + ---------|
   |             2|
   \     -5 + 3*x /
-------------------
 /        2\       
 \-5 + 3*x /*log(5)

$$- \frac{6 \cdot \left(\frac{6 x^{2}}{3 x^{2} - 5} - 1\right)}{\left(3 x^{2} - 5\right) \log{\left(5 \right)}}$$

Simplify

The third derivative [src]

      /           2  \
      |        4*x   |
108*x*|-1 + ---------|
      |             2|
      \     -5 + 3*x /
----------------------
            2         
 /        2\          
 \-5 + 3*x / *log(5)

$$\frac{108 x \left(\frac{4 x^{2}}{3 x^{2} - 5} - 1\right)}{\left(3 x^{2} - 5\right)^{2} \log{\left(5 \right)}}$$

Simplify

The graph

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Derivative of y=log5(3x^2-5)

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The solution