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y=sin4x+cos5x

Derivatives y=sin4x+cos5x

Function f() - derivative -N order

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sin(4*x) + cos(5*x)
$$\sin{\left(4 x \right)} + \cos{\left(5 x \right)}$$
sin(4*x) + cos(5*x)
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. 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:

    The result is:


The answer is:

The graph
The first derivative [src]
-5*sin(5*x) + 4*cos(4*x)
$$- 5 \sin{\left(5 x \right)} + 4 \cos{\left(4 x \right)}$$
The second derivative [src]
-(16*sin(4*x) + 25*cos(5*x))
$$- (16 \sin{\left(4 x \right)} + 25 \cos{\left(5 x \right)})$$
The third derivative [src]
-64*cos(4*x) + 125*sin(5*x)
$$125 \sin{\left(5 x \right)} - 64 \cos{\left(4 x \right)}$$
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