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Derivative of:
Derivative of 2*cos(3*x)
Derivative of 1^3*sqrt(x)
Derivative of (x+4)/(x-1)
Derivative of (x-3)^4
Identical expressions
log(six *sqrt(x))
logarithm of (6 multiply by square root of (x))
logarithm of (six multiply by square root of (x))
log(6*√(x))
log(6sqrt(x))
log6sqrtx
Similar expressions
log(6^sqrt(x))

The derivative of the function/ log(6*sqrt(x))

Derivative of log(6*sqrt(x))

The solution

You have entered [src]

   /    ___\
log\6*\/ x /

$$\log{\left(6 \sqrt{x} \right)}$$

log(6*sqrt(x))

Detail solution

Let $u = 6 \sqrt{x}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} 6 \sqrt{x}$ :
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  So, the result is: $\frac{3}{\sqrt{x}}$
The result of the chain rule is:

$\frac{1}{2 x}$

The answer is:

$\frac{1}{2 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 1 
---
2*x

$$\frac{1}{2 x}$$

Simplify

The second derivative [src]

-1  
----
   2
2*x

$$- \frac{1}{2 x^{2}}$$

Simplify

The third derivative [src]

1 
--
 3
x

$$\frac{1}{x^{3}}$$

Simplify

The graph

Derivative of log(6*sqrt(x))