3. Determine the derivative of each of the following AND simplify FULLY! a. f(x)=. 2x³-1 x² 2 b. y=(7x²+4x+1)³ 3 d. f(x) = x² f(x) = x²² 3 y= (x-2)³ (x²+9)* C. y=(x*)2* f. y = (sin 2x)e³x

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.

Use the product rule to find the derivative of the function. y=(3x²+5) (2x-5) What is the correct way of writing the derivative of y? dy d OA. (3x²+5) (2x-5) dx (3x²+5)•(2x-5) = (3x² +5) • (2x-5) + (2x-5) • (3x²+5) dy O B. dx dy O c. dx dy d ( = (3x² +5) • (2x-5) + (2x-5)•(3x²+5) ○ D. dy dx dx = 則 dx d dx dx d d dx - (3x² +5) • 1x (2x-5)+ + (2x-5) • (3x²+5) dx dx

When applying derivative rules, we sometimes need to rewrite our function. In this problem, you are not computing derivatives. You are only reviewing the skills necessary to rewrite the expression in an equivalent form. (a) Which is equivalent to 1 10 10x-3 -3 X (c) Which is equivalent to 10x + 3x 1 1 10x3 (b) Which is equivalent to ¹x10 ? O x11/10 O x10/11 O 10x + 3 ? 10x² + 3? X (d) Which is equivalent to √x(x-10√x)? O x3/2 - 10x O x3/2 - 10x1/2