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Derivative of:
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Identical expressions
3sin(t/a)+cos(pi/ seventeen)
3 sinus of (t divide by a) plus co sinus of e of ( Pi divide by 17)
3 sinus of (t divide by a) plus co sinus of e of ( Pi divide by seventeen)
3sint/a+cospi/17
3sin(t divide by a)+cos(pi divide by 17)
Similar expressions
3sin(t/a)-cos(pi/17)

The derivative of the function/ 3sin(t/a)+cos(pi/17)

Derivative of 3sin(t/a)+cos(pi/17)

The solution

You have entered [src]

     /t\      /pi\
3*sin|-| + cos|--|
     \a/      \17/

$$3 \sin{\left(\frac{t}{a} \right)} + \cos{\left(\frac{\pi}{17} \right)}$$

d /     /t\      /pi\\
--|3*sin|-| + cos|--||
dt\     \a/      \17//

$$\frac{\partial}{\partial t} \left(3 \sin{\left(\frac{t}{a} \right)} + \cos{\left(\frac{\pi}{17} \right)}\right)$$

Transform

Detail solution

Differentiate $3 \sin{\left(\frac{t}{a} \right)} + \cos{\left(\frac{\pi}{17} \right)}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \frac{t}{a}$ .
  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 $\frac{\partial}{\partial t} \frac{t}{a}$ :
    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: $\frac{1}{a}$
    The result of the chain rule is:
    
    $\frac{\cos{\left(\frac{t}{a} \right)}}{a}$
  So, the result is: $\frac{3 \cos{\left(\frac{t}{a} \right)}}{a}$
2. Let $u = \frac{\pi}{17}$ .
3. The derivative of cosine is negative sine:
  
  $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
4. Then, apply the chain rule. Multiply by $\frac{d}{d t} \frac{\pi}{17}$ :
  1. The derivative of the constant $\frac{\pi}{17}$ is zero.
  The result of the chain rule is:
  
  $0$
The result is: $\frac{3 \cos{\left(\frac{t}{a} \right)}}{a}$

The answer is:

$\frac{3 \cos{\left(\frac{t}{a} \right)}}{a}$

The first derivative [src]

     /t\
3*cos|-|
     \a/
--------
   a

$$\frac{3 \cos{\left(\frac{t}{a} \right)}}{a}$$

Simplify

The second derivative [src]

      /t\
-3*sin|-|
      \a/
---------
     2   
    a

$$- \frac{3 \sin{\left(\frac{t}{a} \right)}}{a^{2}}$$

Simplify

The third derivative [src]

      /t\
-3*cos|-|
      \a/
---------
     3   
    a

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

Simplify