Mister Exam

Derivative of z=y4sin5x+2x−2

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
y4*sin(5*x) + 2*x - 2
$$\left(2 x + y_{4} \sin{\left(5 x \right)}\right) - 2$$
y4*sin(5*x) + 2*x - 2
Detail solution
  1. Differentiate term by term:

    1. Differentiate term by term:

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

        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:

        So, 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. The derivative of the constant is zero.

    The result is:


The answer is:

The first derivative [src]
2 + 5*y4*cos(5*x)
$$5 y_{4} \cos{\left(5 x \right)} + 2$$
The second derivative [src]
-25*y4*sin(5*x)
$$- 25 y_{4} \sin{\left(5 x \right)}$$
The third derivative [src]
-125*y4*cos(5*x)
$$- 125 y_{4} \cos{\left(5 x \right)}$$
3-я производная [src]
-125*y4*cos(5*x)
$$- 125 y_{4} \cos{\left(5 x \right)}$$