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Derivative of:
Derivative of x^-(4/5)
Derivative of sec2x
Derivative of x^2*tgx
Derivative of sin(5)^(3)*x
Identical expressions
y=log3((4x)^ two)
y equally logarithm of 3((4x) squared )
y equally logarithm of 3((4x) to the power of two)
y=log3((4x)2)
y=log34x2
y=log3((4x)²)
y=log3((4x) to the power of 2)
y=log34x^2

The derivative of the function/ y=log3((4x)^2)

Derivative of y=log3((4x)^2)

The solution

You have entered [src]

   /     2\
log\(4*x) /
-----------
   log(3)

$$\frac{\log{\left(\left(4 x\right)^{2} \right)}}{\log{\left(3 \right)}}$$

log((4*x)^2)/log(3)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \left(4 x\right)^{2}$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(4 x\right)^{2}$ :
  1. Let $u = 4 x$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 4 x$ :
    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: $4$
    The result of the chain rule is:
    
    $32 x$
  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((4x)^2)