For the equation y = sin(x). Determine (the 123rd derivative of y)

-cos(x)

Step-by-step explanation:

y¹ = cos(x)

y² = -sin(x)

y³ = -cos(x)

y⁴ = sin(x)

Every 4th derivative is sin(x)

123 = 4(30) + 3

y¹²⁰ = sin(x)

y¹²¹ = cos(x)

y¹²² = -sin(x)

y¹²³ = -cos(x)

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

the first option is the answer.