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Derivative of 3*(cos(t)+(t)*sin(t))

Function f() - derivative -N order at the point
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The graph:

from to

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The solution

You have entered [src]
3*(cos(t) + t*sin(t))
$$3 \left(t \sin{\left(t \right)} + \cos{\left(t \right)}\right)$$
3*(cos(t) + t*sin(t))
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    1. Differentiate term by term:

      1. The derivative of cosine is negative sine:

      2. Apply the product rule:

        ; to find :

        1. Apply the power rule: goes to

        ; to find :

        1. The derivative of sine is cosine:

        The result is:

      The result is:

    So, the result is:


The answer is:

The graph
The first derivative [src]
3*t*cos(t)
$$3 t \cos{\left(t \right)}$$
The second derivative [src]
3*(-t*sin(t) + cos(t))
$$3 \left(- t \sin{\left(t \right)} + \cos{\left(t \right)}\right)$$
The third derivative [src]
-3*(2*sin(t) + t*cos(t))
$$- 3 \left(t \cos{\left(t \right)} + 2 \sin{\left(t \right)}\right)$$