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Derivative of:
Derivative of c
Derivative of atan(2/x)
Derivative of asin((x-1)/x)
Derivative of asin(sin(t)/cos(t))
Identical expressions
y=(lnx+ one)^ two
y equally (lnx plus 1) squared
y equally (lnx plus one) to the power of two
y=(lnx+1)2
y=lnx+12
y=(lnx+1)²
y=(lnx+1) to the power of 2
y=lnx+1^2
Similar expressions
y=(lnx-1)^2

The derivative of the function/ y=(lnx+1)^2

Derivative of y=(lnx+1)^2

The solution

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            2
(log(x) + 1)

$$\left(\log{\left(x \right)} + 1\right)^{2}$$

(log(x) + 1)^2

Detail solution

Let $u = \log{\left(x \right)} + 1$ .
Apply the power rule: $u^{2}$ goes to $2 u$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(\log{\left(x \right)} + 1\right)$ :
1. Differentiate $\log{\left(x \right)} + 1$ term by term:
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  2. The derivative of the constant $1$ is zero.
  The result is: $\frac{1}{x}$
The result of the chain rule is:

$\frac{2 \log{\left(x \right)} + 2}{x}$
Now simplify:

$\frac{2 \left(\log{\left(x \right)} + 1\right)}{x}$

The answer is:

$\frac{2 \left(\log{\left(x \right)} + 1\right)}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2*(log(x) + 1)
--------------
      x

$$\frac{2 \left(\log{\left(x \right)} + 1\right)}{x}$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

2*(-1 + 2*log(x))
-----------------
         3       
        x

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

Simplify

The graph

Derivative of y=(lnx+1)^2