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Derivative of:
Derivative of tan(x/2)
Derivative of e^(7*x)
Derivative of (x^2)
Derivative of tan(x^3)
Identical expressions
-cos(three *x)-sin(three *x)
minus co sinus of e of (3 multiply by x) minus sinus of (3 multiply by x)
minus co sinus of e of (three multiply by x) minus sinus of (three multiply by x)
-cos(3x)-sin(3x)
-cos3x-sin3x
Similar expressions
-cos(3*x)+sin(3*x)
cos(3*x)-sin(3*x)

The derivative of the function/ -cos(3*x)-sin(3*x)

Derivative of -cos(3x)-sin(3x)

The solution

You have entered [src]

-cos(3*x) - sin(3*x)

$$- \sin{\left(3 x \right)} - \cos{\left(3 x \right)}$$

-cos(3*x) - sin(3*x)

Detail solution

Differentiate $- \sin{\left(3 x \right)} - \cos{\left(3 x \right)}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 3 x$ .
  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 $\frac{d}{d x} 3 x$ :
    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: $3$
    The result of the chain rule is:
    
    $- 3 \sin{\left(3 x \right)}$
  So, the result is: $3 \sin{\left(3 x \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 3 x$ .
  2. The derivative of sine is cosine:
    
    $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 3 x$ :
    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: $3$
    The result of the chain rule is:
    
    $3 \cos{\left(3 x \right)}$
  So, the result is: $- 3 \cos{\left(3 x \right)}$
The result is: $3 \sin{\left(3 x \right)} - 3 \cos{\left(3 x \right)}$
Now simplify:

$- 3 \sqrt{2} \cos{\left(3 x + \frac{\pi}{4} \right)}$

The answer is:

$- 3 \sqrt{2} \cos{\left(3 x + \frac{\pi}{4} \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-3*cos(3*x) + 3*sin(3*x)

$$3 \sin{\left(3 x \right)} - 3 \cos{\left(3 x \right)}$$

Simplify

The second derivative [src]

9*(cos(3*x) + sin(3*x))

$$9 \left(\sin{\left(3 x \right)} + \cos{\left(3 x \right)}\right)$$

Simplify

The third derivative [src]

27*(-sin(3*x) + cos(3*x))

$$27 \left(- \sin{\left(3 x \right)} + \cos{\left(3 x \right)}\right)$$

Simplify