Mister Exam

Derivative of sin4x+cos(3x-3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
sin(4*x) + cos(3*x - 3)
$$\sin{\left(4 x \right)} + \cos{\left(3 x - 3 \right)}$$
sin(4*x) + cos(3*x - 3)
Detail solution
  1. Differentiate term by term:

    1. Let .

    2. The derivative of sine is cosine:

    3. Then, apply the chain rule. Multiply by :

      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:

      The result of the chain rule is:

    4. Let .

    5. The derivative of cosine is negative sine:

    6. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        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:

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
-3*sin(3*x - 3) + 4*cos(4*x)
$$- 3 \sin{\left(3 x - 3 \right)} + 4 \cos{\left(4 x \right)}$$
The second derivative [src]
-(9*cos(3*(-1 + x)) + 16*sin(4*x))
$$- (16 \sin{\left(4 x \right)} + 9 \cos{\left(3 \left(x - 1\right) \right)})$$
The third derivative [src]
-64*cos(4*x) + 27*sin(3*(-1 + x))
$$27 \sin{\left(3 \left(x - 1\right) \right)} - 64 \cos{\left(4 x \right)}$$