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y=tg4x-2x^4-10x

Derivative of y=tg4x-2x^4-10x

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

The graph:

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The solution

You have entered [src]
              4       
tan(4*x) - 2*x  - 10*x
$$- 10 x + \left(- 2 x^{4} + \tan{\left(4 x \right)}\right)$$
tan(4*x) - 2*x^4 - 10*x
Detail solution
  1. Differentiate term by term:

    1. Differentiate term by term:

      1. Rewrite the function to be differentiated:

      2. Apply the quotient rule, which is:

        and .

        To find :

        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:

        To find :

        1. Let .

        2. The derivative of cosine is negative sine:

        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:

        Now plug in to the quotient rule:

      3. 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 is:

    2. 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 is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
        3        2     
-6 - 8*x  + 4*tan (4*x)
$$- 8 x^{3} + 4 \tan^{2}{\left(4 x \right)} - 6$$
The second derivative [src]
  /     2     /       2     \         \
8*\- 3*x  + 4*\1 + tan (4*x)/*tan(4*x)/
$$8 \left(- 3 x^{2} + 4 \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan{\left(4 x \right)}\right)$$
The third derivative [src]
   /                        2                               \
   |         /       2     \          2      /       2     \|
16*\-3*x + 8*\1 + tan (4*x)/  + 16*tan (4*x)*\1 + tan (4*x)//
$$16 \left(- 3 x + 8 \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} + 16 \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan^{2}{\left(4 x \right)}\right)$$
3-я производная [src]
   /                        2                               \
   |         /       2     \          2      /       2     \|
16*\-3*x + 8*\1 + tan (4*x)/  + 16*tan (4*x)*\1 + tan (4*x)//
$$16 \left(- 3 x + 8 \left(\tan^{2}{\left(4 x \right)} + 1\right)^{2} + 16 \left(\tan^{2}{\left(4 x \right)} + 1\right) \tan^{2}{\left(4 x \right)}\right)$$
The graph
Derivative of y=tg4x-2x^4-10x