Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^5
Derivative of x⁴
Derivative of sh(x)
Derivative of f(x)=2x^3
Graphing y =:
cos(x+pi/3)-1
Identical expressions
cos(x+pi/ three)- one
co sinus of e of (x plus Pi divide by 3) minus 1
co sinus of e of (x plus Pi divide by three) minus one
cosx+pi/3-1
cos(x+pi divide by 3)-1
Similar expressions
cos(x+pi/3)+1
cos(x-pi/3)-1
What you mean?
cos((x + pi)/3) - 1*1
cos(x + pi/3) - 1*1
cos(x + pi/3) - 1*1

The derivative of the function/ cos(x+pi/3)-1

You entered:

cos(x+pi/3)-1

What you mean?

cos((x + pi)/3) - 1*1

cos(x + pi/3) - 1*1

cos(x + pi/3) - 1*1

Derivative of cos(x+pi/3)-1

The solution

You have entered [src]

   /    pi\    
cos|x + --| - 1
   \    3 /

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

d /   /    pi\    \
--|cos|x + --| - 1|
dx\   \    3 /    /

$$\frac{d}{d x} \left(\cos{\left(x + \frac{\pi}{3} \right)} - 1\right)$$

Transform

Detail solution

Differentiate $\cos{\left(x + \frac{\pi}{3} \right)} - 1$ term by term:
1. Let $u = x + \frac{\pi}{3}$ .
2. The derivative of cosine is negative sine:
  
  $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + \frac{\pi}{3}\right)$ :
  1. Differentiate $x + \frac{\pi}{3}$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $\frac{\pi}{3}$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $- \sin{\left(x + \frac{\pi}{3} \right)}$
4. The derivative of the constant $\left(-1\right) 1$ is zero.
The result is: $- \sin{\left(x + \frac{\pi}{3} \right)}$

The answer is:

$- \sin{\left(x + \frac{\pi}{3} \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    /    pi\
-sin|x + --|
    \    3 /

$$- \sin{\left(x + \frac{\pi}{3} \right)}$$

Simplify

The second derivative [src]

    /    pi\
-cos|x + --|
    \    3 /

$$- \cos{\left(x + \frac{\pi}{3} \right)}$$

Simplify

The third derivative [src]

   /    pi\
sin|x + --|
   \    3 /

$$\sin{\left(x + \frac{\pi}{3} \right)}$$

Simplify

The graph

Derivative of cos(x+pi/3)-1