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Derivative of:
Derivative of (x+4)/(x-1)
Derivative of x^2-7*x
Derivative of x^2+4x
Derivative of ln(1+x)
Identical expressions
(five *y-sin(y))/ three
(5 multiply by y minus sinus of (y)) divide by 3
(five multiply by y minus sinus of (y)) divide by three
(5y-sin(y))/3
5y-siny/3
(5*y-sin(y)) divide by 3
Similar expressions
(5*y+sin(y))/3

The derivative of the function/ (5*y-sin(y))/3

Derivative of (5*y-sin(y))/3

The solution

You have entered [src]

5*y - sin(y)
------------
     3

$$\frac{5 y - \sin{\left(y \right)}}{3}$$

(5*y - sin(y))/3

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $5 y - \sin{\left(y \right)}$ 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: $y$ goes to $1$
    So, the result is: $5$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of sine is cosine:
      
      $\frac{d}{d y} \sin{\left(y \right)} = \cos{\left(y \right)}$
    So, the result is: $- \cos{\left(y \right)}$
  The result is: $5 - \cos{\left(y \right)}$
So, the result is: $\frac{5}{3} - \frac{\cos{\left(y \right)}}{3}$

The answer is:

$\frac{5}{3} - \frac{\cos{\left(y \right)}}{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

5   cos(y)
- - ------
3     3

$$\frac{5}{3} - \frac{\cos{\left(y \right)}}{3}$$

Simplify

The second derivative [src]

sin(y)
------
  3

$$\frac{\sin{\left(y \right)}}{3}$$

Simplify

The third derivative [src]

cos(y)
------
  3

$$\frac{\cos{\left(y \right)}}{3}$$

Simplify