Mister Exam

Derivative of 3x*sinx

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
3*x*sin(x)
$$3 x \sin{\left(x \right)}$$
(3*x)*sin(x)
Detail solution
  1. Apply the product rule:

    ; to find :

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

      1. Apply the power rule: goes to

      So, the result is:

    ; to find :

    1. The derivative of sine is cosine:

    The result is:


The answer is:

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