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y=√sin²*5x/x³+1

How to use it?
Derivative of:
Derivative of 2*x-x^2
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Derivative of x*(1-x)
Derivative of log(1+e^x)
Identical expressions
y=√sin²*5x/x³+ one
y equally √ sinus of ² multiply by 5x divide by x³ plus 1
y equally √ sinus of ² multiply by 5x divide by x³ plus one
y=√sin²5x/x³+1
y=√sin²*5x divide by x³+1
Similar expressions
y=√sin²*5x/x³-1

The derivative of the function/ y=√sin²*5x/x³+1

Derivative of y=√sin²*5x/x³+1

The solution

You have entered [src]

          2      
  ________       
\/ sin(5)  *x    
------------- + 1
       3         
      x

$$1 + \frac{x \left(\sqrt{\sin{\left(5 \right)}}\right)^{2}}{x^{3}}$$

((sqrt(sin(5)))^2*x)/x^3 + 1

Detail solution

Differentiate $1 + \frac{x \left(\sqrt{\sin{\left(5 \right)}}\right)^{2}}{x^{3}}$ term by term:
1. Apply the quotient rule, which is:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = x \sin{\left(5 \right)}$ and $g{\left(x \right)} = x^{3}$ .
  
  To find $\frac{d}{d x} f{\left(x \right)}$ :
  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: $\sin{\left(5 \right)}$
  To find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  Now plug in to the quotient rule:
  
  $- \frac{2 \sin{\left(5 \right)}}{x^{3}}$
2. The derivative of the constant $1$ is zero.
The result is: $- \frac{2 \sin{\left(5 \right)}}{x^{3}}$

The answer is:

$- \frac{2 \sin{\left(5 \right)}}{x^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*sin(5)
---------
     3   
    x

$$- \frac{2 \sin{\left(5 \right)}}{x^{3}}$$

Simplify

The second derivative [src]

6*sin(5)
--------
    4   
   x

$$\frac{6 \sin{\left(5 \right)}}{x^{4}}$$

Simplify

The third derivative [src]

-24*sin(5)
----------
     5    
    x

$$- \frac{24 \sin{\left(5 \right)}}{x^{5}}$$

Simplify

The graph

Derivative of y=√sin²*5x/x³+1