Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^-2
Derivative of (-1)/x^2
Derivative of e^x^3
Derivative of (x+1)
Integral of d{x}:
1/3+2cosx-sinx
Identical expressions
one / three +2cosx-sinx
1 divide by 3 plus 2 co sinus of e of x minus sinus of x
one divide by three plus 2 co sinus of e of x minus sinus of x
1 divide by 3+2cosx-sinx
Similar expressions
1/3-2cosx-sinx
1/3+2cosx+sinx

The derivative of the function/ 1/3+2cosx-sinx

Derivative of 1/3+2cosx-sinx

The solution

You have entered [src]

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

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

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

Detail solution

Differentiate $\left(2 \cos{\left(x \right)} + \frac{1}{3}\right) - \sin{\left(x \right)}$ term by term:
1. Differentiate $2 \cos{\left(x \right)} + \frac{1}{3}$ term by term:
  1. The derivative of the constant $\frac{1}{3}$ is zero.
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of cosine is negative sine:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
    So, the result is: $- 2 \sin{\left(x \right)}$
  The result is: $- 2 \sin{\left(x \right)}$
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:
    
    $\frac{d}{d x} \sin{\left(x \right)} = \cos{\left(x \right)}$
  So, the result is: $- \cos{\left(x \right)}$
The result is: $- 2 \sin{\left(x \right)} - \cos{\left(x \right)}$

The answer is:

$- 2 \sin{\left(x \right)} - \cos{\left(x \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-cos(x) - 2*sin(x)

$$- 2 \sin{\left(x \right)} - \cos{\left(x \right)}$$

Simplify

The second derivative [src]

-2*cos(x) + sin(x)

$$\sin{\left(x \right)} - 2 \cos{\left(x \right)}$$

Simplify

The third derivative [src]

2*sin(x) + cos(x)

$$2 \sin{\left(x \right)} + \cos{\left(x \right)}$$

Simplify