I Determine dy/dx for each of the following functions, Express the answers in simplified form

I Determine dy/dx for each of the following functions, Express the answers in simplified form.

  a. y=6x⁴-3x² + 5x² -1

  b. Y = √16x³

c. Use the derivative of Y = 4√x3 to determine of its slope of the tangent drawn at P(4,32)

II a) Determine the derivative of the function, write the answer in the most simplified form.

    S(t) = (t²+ 1) (3 – 2r²)

b) Use the derivative to determine point(s) where the tangent to the curve is horizontal.

III a) Determine the derivative of the function = x³/x²-6 , Write the answer in the most simplified form possible

b) Find the Equation of the tangent to the graph of the function, drawn at the point Q (3,9)

IV – Determine a formula for the product rule in the case where we are asked to differentiate the product of four functions. That is, if y = m(x)p(x) q (x) r (x), determine a formula for dy/dx