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The derivative of the function/ а(sint-tcost)

Derivative of а(sint-tcost)

Function f() - derivative -N order at the point
v

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from to

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The solution

You have entered [src] 
a*(sin(t) - tcost)
a(−tcost+sin⁡(t))a \left(- tcost + \sin{\left(t \right)}\right) 
d                     
--(a*(sin(t) - tcost))
dt
∂∂ta(−tcost+sin⁡(t))\frac{\partial}{\partial t} a \left(- tcost + \sin{\left(t \right)}\right)
Transform
Detail solution

  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Differentiate −tcost+sin⁡(t)- tcost + \sin{\left(t \right)} term by term:

      1. The derivative of sine is cosine:

        ddtsin⁡(t)=cos⁡(t)\frac{d}{d t} \sin{\left(t \right)} = \cos{\left(t \right)}

      2. The derivative of the constant −tcost- tcost is zero.

      The result is: cos⁡(t)\cos{\left(t \right)}

    So, the result is: acos⁡(t)a \cos{\left(t \right)}

The answer is:

acos⁡(t)a \cos{\left(t \right)}

The first derivative [src] 
a*cos(t)
acos⁡(t)a \cos{\left(t \right)}
Simplify
The second derivative [src] 
-a*sin(t)
−asin⁡(t)- a \sin{\left(t \right)}
Simplify
The third derivative [src] 
-a*cos(t)
−acos⁡(t)- a \cos{\left(t \right)}
Simplify
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