Zenzizenzicube is an obsolete word that represents the square of the square of a cube. In symbols, zenzizenzicube is written as (((x^3)^2))^2

Required:
a. Use the chain rule twice to find the derivative.
b. Use the properties of exponents to first simplify the expression, and then find the derivative.

Step-by-step explanation:

Given the expression (((x^3)^2))^2

a) Differentiating the function with respect to x using chain rule.

Given y = (((x^3)^2))^2

Let u = (x³)²

y = u²; dy/du = 2u

Let p = x³; dp/dx = 3x²

u = p²; du/dp = 2p

Applying the chain rule formula:

dy/dx = dy/du • du/dp • dp/dx

substitute in the formula

dy/dx = 2u•2p•3x²

Since u = (x³)² and p = x³

dy/dx = 2(x³)²(2x³)(3x²)

dy/dx = 12x^6•x^5

dy/dx = 12x¹¹

b) Using property of exponent

y = (((x^3)^2))^2

y = (x^6)²

y = x¹²

dy/dx = 12x^12-1

dy/dx = 12x^11

sup

step-by-step explanation:

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .