Find the derivation of the following functions with they corresponding variables

d(f(t))/dt = –56/(t^8) – (5/6)/t^(7/6) + 12t^3 – 2t + (1/3)t^(2/3))

Step-by-step explanation:

To find the derivative of f(t), we have to find the derivative of each component of the function to make it easier.

d(8/(t^7))/dt = d(8xt^-7)/dt = –7 x 8 x t^-8 = –56t^-8 = -56/(t^8)

d(5/(t^(1/6)))/dt = –(1/6) x 5 x t^(-7/6) = –(5/6)/t^(7/6)

d(3t^4)/dt = 4 x 3 x t^3 = 12t^3

d(t²)/dt = 2t

d(t^⅓)/dt = ⅓t^(-2/3) = (1/3)t^(2/3))

d(12)/dt = 0.

Therefore,

d(f(t))/dt = –56/(t^8) – (5/6)/t^(7/6) + 12t^3 – 2t + (1/3)t^(2/3))

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.