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Derivative of:
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Identical expressions
three *sin(t)-sin(3t)
3 multiply by sinus of (t) minus sinus of (3t)
three multiply by sinus of (t) minus sinus of (3t)
3sin(t)-sin(3t)
3sint-sin3t
Similar expressions
3*sin(t)+sin(3t)

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

Derivative of 3*sin(t)-sin(3t)

The solution

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3*sin(t) - sin(3*t)

$$3 \sin{\left(t \right)} - \sin{\left(3 t \right)}$$

3*sin(t) - sin(3*t)

Detail solution

Differentiate $3 \sin{\left(t \right)} - \sin{\left(3 t \right)}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of sine is cosine:
    
    $\frac{d}{d t} \sin{\left(t \right)} = \cos{\left(t \right)}$
  So, the result is: $3 \cos{\left(t \right)}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 3 t$ .
  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 $\frac{d}{d t} 3 t$ :
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $t$ goes to $1$
      So, the result is: $3$
    The result of the chain rule is:
    
    $3 \cos{\left(3 t \right)}$
  So, the result is: $- 3 \cos{\left(3 t \right)}$
The result is: $3 \cos{\left(t \right)} - 3 \cos{\left(3 t \right)}$

The answer is:

$3 \cos{\left(t \right)} - 3 \cos{\left(3 t \right)}$

The graph

Plot the graph f(x)

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The first derivative [src]

-3*cos(3*t) + 3*cos(t)

$$3 \cos{\left(t \right)} - 3 \cos{\left(3 t \right)}$$

Simplify

The second derivative [src]

3*(-sin(t) + 3*sin(3*t))

$$3 \left(- \sin{\left(t \right)} + 3 \sin{\left(3 t \right)}\right)$$

Simplify

The third derivative [src]

3*(-cos(t) + 9*cos(3*t))

$$3 \left(- \cos{\left(t \right)} + 9 \cos{\left(3 t \right)}\right)$$

Simplify