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Derivative of:
Derivative of x^12
Derivative of -e^x
Derivative of e^(2-x)
Derivative of x^2-4*x
Identical expressions
log0. five (sqrt((three *x+ one)))
logarithm of 0.5( square root of ((3 multiply by x plus 1)))
logarithm of 0. five ( square root of ((three multiply by x plus one)))
log0.5(√((3*x+1)))
log0.5(sqrt((3x+1)))
log0.5sqrt3x+1
Similar expressions
log0.5(sqrt((3*x-1)))

The derivative of the function/ log0.5(sqrt((3*x+1)))

Derivative of log0.5(sqrt((3*x+1)))

The solution

You have entered [src]

             _________
log(0.0)*5*\/ 3*x + 1

$$5 \log{\left(0.0 \right)} \sqrt{3 x + 1}$$

(log(0.0)*5)*sqrt(3*x + 1)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 3 x + 1$ .
2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(3 x + 1\right)$ :
  1. Differentiate $3 x + 1$ 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: $x$ goes to $1$
      So, the result is: $3$
    2. The derivative of the constant $1$ is zero.
    The result is: $3$
  The result of the chain rule is:
  
  $\frac{3}{2 \sqrt{3 x + 1}}$
So, the result is: $\frac{15 \log{\left(0.0 \right)}}{2 \sqrt{3 x + 1}}$
Now simplify:

$\frac{\tilde{\infty}}{\sqrt{3 x + 1}}$

The answer is:

$\frac{\tilde{\infty}}{\sqrt{3 x + 1}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 15*log(0.0) 
-------------
    _________
2*\/ 3*x + 1

$$\frac{15 \log{\left(0.0 \right)}}{2 \sqrt{3 x + 1}}$$

Simplify

The second derivative [src]

 -45*log(0.0) 
--------------
           3/2
4*(1 + 3*x)

$$- \frac{45 \log{\left(0.0 \right)}}{4 \left(3 x + 1\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

 405*log(0.0) 
--------------
           5/2
8*(1 + 3*x)

$$\frac{405 \log{\left(0.0 \right)}}{8 \left(3 x + 1\right)^{\frac{5}{2}}}$$

Simplify