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Derivative of:
Derivative of x^2*e^2
Derivative of y=x(x-1)
Derivative of y=5+12x-x³
Derivative of y=1/2
Identical expressions
five *sin(pi*t)/ two
5 multiply by sinus of ( Pi multiply by t) divide by 2
five multiply by sinus of ( Pi multiply by t) divide by two
5sin(pit)/2
5sinpit/2
5*sin(pi*t) divide by 2

The derivative of the function/ 5*sin(pi*t)/2

Derivative of 5sin(pit)/2

The solution

You have entered [src]

5*sin(pi*t)
-----------
     2

$$\frac{5 \sin{\left(\pi t \right)}}{2}$$

(5*sin(pi*t))/2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \pi t$ .
  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 $\frac{d}{d t} \pi t$ :
    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: $\pi$
    The result of the chain rule is:
    
    $\pi \cos{\left(\pi t \right)}$
  So, the result is: $5 \pi \cos{\left(\pi t \right)}$
So, the result is: $\frac{5 \pi \cos{\left(\pi t \right)}}{2}$

The answer is:

$\frac{5 \pi \cos{\left(\pi t \right)}}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

5*pi*cos(pi*t)
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      2

$$\frac{5 \pi \cos{\left(\pi t \right)}}{2}$$

Simplify

The second derivative [src]

     2          
-5*pi *sin(pi*t)
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       2

$$- \frac{5 \pi^{2} \sin{\left(\pi t \right)}}{2}$$

Simplify

The third derivative [src]

     3          
-5*pi *cos(pi*t)
----------------
       2

$$- \frac{5 \pi^{3} \cos{\left(\pi t \right)}}{2}$$

Simplify