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Derivative of:
Derivative of (-6)/x^4
Derivative of ln(x^2-2x)
Derivative of 6/x^4
Derivative of 5/x^3
Identical expressions
y=x^ three +sinx+lnx
y equally x cubed plus sinus of x plus lnx
y equally x to the power of three plus sinus of x plus lnx
y=x3+sinx+lnx
y=x³+sinx+lnx
y=x to the power of 3+sinx+lnx
Similar expressions
y=x^3-sinx+lnx
y=x^3+sinx-lnx

The derivative of the function/ y=x^3+sinx+lnx

Derivative of y=x^3+sinx+lnx

The solution

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 3                  
x  + sin(x) + log(x)

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

x^3 + sin(x) + log(x)

Detail solution

Differentiate $\left(x^{3} + \sin{\left(x \right)}\right) + \log{\left(x \right)}$ term by term:
1. Differentiate $x^{3} + \sin{\left(x \right)}$ term by term:
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  2. The derivative of sine is cosine:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  The result is: $3 x^{2} + \cos{\left(x \right)}$
2. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
The result is: $3 x^{2} + \cos{\left(x \right)} + \frac{1}{x}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  1                
- -- - sin(x) + 6*x
   2               
  x

$$6 x - \sin{\left(x \right)} - \frac{1}{x^{2}}$$

Simplify

The third derivative [src]

             2 
6 - cos(x) + --
              3
             x

$$- \cos{\left(x \right)} + 6 + \frac{2}{x^{3}}$$

Simplify

The graph

Derivative of y=x^3+sinx+lnx