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Derivative of:
Derivative of tanh(x)
Derivative of cos²x
Derivative of (π-2x)³
Derivative of log(x)+(x+1)^3
Identical expressions
log(x)+(x+ one)^ three
logarithm of (x) plus (x plus 1) cubed
logarithm of (x) plus (x plus one) to the power of three
log(x)+(x+1)3
logx+x+13
log(x)+(x+1)³
log(x)+(x+1) to the power of 3
logx+x+1^3
Similar expressions
log(x)+(x-1)^3
log(x)-(x+1)^3

The derivative of the function/ log(x)+(x+1)^3

Derivative of log(x)+(x+1)^3

The solution

You have entered [src]

                3
log(x) + (x + 1)

$$\left(x + 1\right)^{3} + \log{\left(x \right)}$$

log(x) + (x + 1)^3

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

    1       
6 - -- + 6*x
     2      
    x

$$6 x + 6 - \frac{1}{x^{2}}$$

Simplify

The third derivative [src]

  /    1 \
2*|3 + --|
  |     3|
  \    x /

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

Simplify

The graph

Derivative of log(x)+(x+1)^3