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Derivative of:
Derivative of arcsec(x)
Derivative of y=sqrt(cos3x)
Derivative of y=log3(5x^2)
Derivative of y=ln(tg(x)+ctg(x))/(sin(a))
Identical expressions
y=log3(5x^ two)
y equally logarithm of 3(5x squared )
y equally logarithm of 3(5x to the power of two)
y=log3(5x2)
y=log35x2
y=log3(5x²)
y=log3(5x to the power of 2)
y=log35x^2

The derivative of the function/ y=log3(5x^2)

Derivative of y=log3(5x^2)

The solution

You have entered [src]

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

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

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

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

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 5 x^{2}$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 5 x^{2}$ :
  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: $10 x$
  The result of the chain rule is:
  
  $\frac{2}{x}$
So, the result is: $\frac{2}{x \log{\left(3 \right)}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   2    
--------
x*log(3)

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

Simplify

The second derivative [src]

   -2    
---------
 2       
x *log(3)

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

Simplify

The third derivative [src]

    4    
---------
 3       
x *log(3)

$$\frac{4}{x^{3} \log{\left(3 \right)}}$$

Simplify

The graph

Derivative of y=log3(5x^2)