Yequals(9 x Superscript 4 Baseline minus 4 x squared plus 6 )Superscript 4 To find StartFraction dy Over dx EndFraction , write y as a function of u so that yequalsf(u) and uequalsg(x). What is uequalsg(x) in this case?

Step-by-step explanation:

Given the function

y = (9x⁴ — 4x² + 6)⁴

We need to find the derivative of y with respect to x i.e. dy/dx.

So let u = 9x⁴—4x² + 6

Then y = u²,

Then, y is a function of u, y=f(u)

Also, u is a function of x, u = g(x)

In this case,

u = g(x) = 9x⁴—4x² + 6

So let differentiate this function y(x).

This is a function of a function

Then, we need to find u'(x)

u (x) = 9x⁴—4x² + 6

Then, u'(x) = 36x³ — 8x

Also we need to find y'(u)

Then, y = u²

y'(u) = 2u

Using function of a function formula

dy / dx = dy/du × du/dx

y'(x) = y'(u) × u'(x)

y'(x) = 2u × 36x³ — 8x

y'(x) = 2u(36x³ — 8x)

Since, u = 9x⁴—4x² + 6

Therefore,

y'(t) = 2(9x⁴—4x² + 6)(36x³ — 8x)

So,

dy/dx = 2(9x⁴—4x² + 6)(36x³ — 8x)

dy/dx = (18x⁴—8x² + 12)(36x³ — 8x)

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.